discrete breathers in thermal equilibrium distributions and energy gaps we study a discrete two dimensional nonlinear system that allows for discrete breather solutions we perform a spectral analysis of the lattice dynamics at thermal equilibrium and use a cooling technique to measure the amount of breathers at thermal equilibrium our results confirm the existence of an energy threshold for discrete breathers the cooling method provides a novel way of measuring and analyzing discrete breather distribution properties in thermal equilibrium

discrete solitons in nonlinear schrodinger lattices with a power law nonlinearity abstract we study the discrete nonlinear schrodinger lattice model with the onsite nonlinearity of the general form u 2 u we systematically verify the conditions for the existence and stability of discrete solitons in the one dimensional version of the model predicted by means of the variational approximation va and demonstrate the following monostability of fundamental solitons fss in the case of the weak nonlinearity 2 1 3 68 bistability in a finite range of values of the soliton s power for 3 68 2 1 5 and the presence of a threshold minimum norm of the fs for 2 1 5 we also perform systematic numerical simulations to study higher order solitons in the same general model i e bound states of the fss while all in phase bound states are unstable stability regions are identified for antisymmetric double solitons and their triple counterparts these numerical findings are supplemented by an analytical treatment of the stability problem which allows quantitively accurate predictions for the stability features of such multipulses when these waveforms are found to be unstable we show by means of direct simulations that they self trap into a persistent lattice breather or relax into a stable fs or sometimes decay completely

stability of discrete breathers abstract we approach the problem of linear stability of discrete breathers in a rigorous way for networks of not necessarily identical oscillators with general type of coupling in the case of hamiltonian systems using symplectic signature theory we give general conditions on the spectrum of the monodromy map in the uncoupled limit such that the discrete breathers are l 2 linearly stable for weak enough coupling we consider also dissipative networks of oscillators in this case we prove that the discrete breathers are not only stable but also attract a neighbourhood of initial data for any choice of l p topology some examples are considered amongst which an instance of roto breather

diffusion of intrinsic localized modes by attractor hopping propagating intrinsic localized modes exist in the damped driven discrete sine gordon chain as attractors of the dynamics the equations of motion of the system are augmented with gaussian white noise in order to model the effects of temperature on the system the noise induces random transitions between attracting configurations corresponding to opposite signs of the propagation velocity of the mode which leads to a diffusive motion of the excitation the heun method is used to numerically generate the stochastic time evolution of the configuration we also present a theoretical model for the diffusion which contains two parameters a transition probability and a delay time a the mean value and the variance of the position of the intrinsic localized mode obtained from simulations can be fitted well with the predictions of our model and a being used as parameters in the fit after a transition period following the switching on of the noise the variance shows a linear behaviour as a function of time and the mean value remains constant an increase in the strength of the noise lowers the variance leads to an increase in a decrease in a and reduces the average distance a mode travels during the transition period

on the dynamics of the holstein model from the anticontinuous limit we consider the holstein model describing an electron interacting with a lattice of identical oscillators we remark that the on site system i e the system in which the interaction between the different sites of the lattice vanishes is integrable and anisocronous this allows us to apply some recent nekhoroshev type results to show that corresponding to the majority of initial data in which the electron probability is concentrated on a finite number of sites the electron probability distribution is approximatively constant for times growing exponentially with the inverse of the coupling parameter moreover for the same times the total energy of the oscillator system is approximatively constant

travelling solitary waves in the discrete schrodinger equation with saturable nonlinearity existence stability and dynamics the present work examines in detail the existence stability and dynamics of travelling solitary waves in a schrodinger lattice with saturable nonlinearity after analysing the linear spectrum of the problem in the travelling wave frame a pseudo spectral numerical method is used to identify weakly nonlocal solitary waves by finding zeros of an appropriately crafted tail condition we can obtain the genuinely localized pulse like solutions subsequent use of continuation methods allows us to obtain the relevant branches of solutions as a function of the system parameters such as the frequency and intersite coupling strength we examine the stability of the solutions in two ways both by imposing numerical perturbations and observing the solution dynamics as well as by considering the solutions as fixed points of an appropriate map and computing the corresponding floquet matrix and its eigenvalues both methods indicate that our solutions are robustly localized finally the interactions of these solutions are examined in collision type phenomena observing that relevant collisions are near elastic although they may under appropriate conditions lead to the generation of an additional pulse

intraband discrete breathers in disordered nonlinear systems ii localization abstract we find spatially localized time periodic solutions discrete breathers or dbs in disordered nonlinear systems with frequency inside the linear phonon spectrum under conditions that strictly prohibit their existence in their periodic counterparts for that purpose we develop a new in situ method for the accurate calculation of these solutions which does not make use of any continuation from an anticontinuous limit using this method we demonstrate that intraband localized modes intraband discrete breathers or idbs at a given site with frequencies inside the discrete linear spectrum do exist provided these frequencies do not belong to forbidden resonance gaps since there is a dense set of resonant frequencies we illustrate numerically in agreement with a theorem by albanese and frohlich that the localized dbs exist provided that their frequencies belong to fat cantor sets i e with finite measure such a set contains as accumulation points the linear frequency of the normal mode at the occupied site we check that many of these solutions are linearly stable and conjecture that their frequency belongs to another smaller fat cantor set our numerical methods provide a much wider set of exact solutions which are multisite breathers and suggest conjectures extending the existing theorems the physical implications of the existence of idbs and possible applications for glasses and the persistent spectral hole burning are discussed

the notion of persistence applied to breathers in thermal equilibrium abstract we study the thermal equilibrium of nonlinear klein gordon chains at the limit of small coupling anticontinuum limit we show that the persistence distribution associated to the local energy density is a useful tool to study the statistical distribution of the so called thermal breathers mainly when the equilibrium is characterized by long lived pinned excitations in that case the distribution of persistence intervals turns out to be a power law we demonstrate also that this generic behaviour has a counterpart in the power spectra where the high frequencies domains nicely collapse if properly rescaled these results are also compared to nonlinear klein gordon chains with a soft nonlinearity for which the thermal breathers are rather mobile entities finally we discuss the possibility of a breather induced anomalous diffusion law and show that despite a strong slowing down of the energy diffusion there are numerical evidences for a normal asymptotic diffusion mechanism but with exceptionally small diffusion coefficients

bifurcation analysis of the localized modes dynamics in lattices with saturable nonlinearity abstract the dynamics of localized modes in discrete media with saturable nonlinearity are investigated the stability of stationary bright solitons is discussed from the view point of the energy minimum principle and mapping analysis due to the cascade saturation mechanism a bifurcation from trapped to transversely moving localized mode is found for particular values of high power the bifurcation coincides with the existence of the almost perfect separatrix in the corresponding area preserving map in addition the definition of the peierls nabarro effective potential is reconsidered

on the existence of homoclinic solutions of a class of discrete nonlinear periodic systems abstract in this paper we obtain a new sufficient condition on the existence of homoclinic solutions of a class of discrete nonlinear periodic systems by using critical point theory in combination with periodic approximations we prove that it is also necessary in some special cases

lyapunov schmidt reduction algorithm for three dimensional discrete vortices abstract we address the persistence and stability of three dimensional vortex configurations in the discrete nonlinear schrodinger equation and develop a symbolic package based on wolfram s mathematica for computations of the lyapunov schmidt reduction method the lyapunov schmidt reduction method is a theoretical tool which enables us to study continuations and terminations of the discrete vortices for small coupling between lattice nodes as well as the spectral stability of the persistent configurations the method was developed earlier in the context of the two dimensional lattice and applied to the onsite and offsite configurations called the vortex cross and the vortex cell by using semianalytical computations d e pelinovsky p g kevrekidis d frantzeskakis physica d 212 2005 20 53 p g kevrekidis d e pelinovsky proc r soc a 462 2006 2671 2694 the present treatment develops a full symbolic computational package which takes a desired waveform at the anticontinuum limit of uncoupled sites performs a required number of lyapunov schmidt reductions and outputs the predictions on whether the configuration persists for finite coupling in the three dimensional lattice and whether it is stable or unstable it also provides approximations for the eigenvalues of the linearized stability problem we report a number of applications of the algorithm to important multisite three dimensional configurations such as the simple cube the double cross and the diamond for each configuration we identify exactly one solution which is stable for small coupling between lattice nodes

linear stability of perturbed hamiltonian systems theory and a case example in this paper we present a general theory based on a lyapunov schmidt reduction for the linearized stability of a perturbed hamiltonian system with a number of symmetries the reduction leads to an eigenvalue problem in a small subspace of the original system whose eigenvalues and eigenvectors can be used to derive the ones of the perturbed original system the krein signature of the eigenvalues can also be obtained in this framework the method is applied to the case example of the coupled nonlinear schr dinger equations giving excellent agreement with the full numerical linear stability results

existence and stability of 3 site breathers in a triangular lattice we find conditions for existence and stability of various types of discrete breather concentrated around three central sites in a triangular lattice of one dimensional hamiltonian oscillators with on site potential and nearest neighbour coupling in particular we confirm that it can support non reversible breather solutions despite the time reversible character of the system they carry a net energy flux and can be called vortex breathers we prove that there are parameter regions for which they are linearly stable for example in a lattice consisting of coupled morse oscillators whereas the related reversible breathers are unstable thus non reversible breathers can be physically relevant

singular limit of a p laplacian reaction diffusion equation with a spatially inhomogeneous reaction term we study singular limit of a p laplacian reaction diffusion equation with a spatially inhomogeneous reaction term the coefficient of the reaction term is much larger than the diffusion coefficient and sharp interfaces appear between two phases we show by matched asymptotic expansions that the limit equation interface equation is a mean curvature flow with drift terms similar to the case p 2

localized breather like solution in a discrete klein gordon model and application to dna abstract non propagating localized oscillating solutions are studied in the case of a discrete one dimensional system with the 2 3 power onsite potential a multiple scale asymptotic perturbation expansion is not adequate for describing the large amplitude oscillations we consider starting from an exact pulse like solution in the continuum we derive an approximate oscillating solution our numerical simulations reveal that whereas the excitations are strongly damped in the strong intersite coupling case they are long lived in the discrete cases an additional modulation phenomenon of the oscillation seen in the simulation is explained by combination of the breather oscillations with the zero group velocity phonons modes then applying the green s functions formalism in analogy with a previous work s takeno et al prog theor phys suppl 94 1988 we derive a very accurate expression for the discrete breather with a quasi infinite lifetime lastly we demonstrate how such excitations can explain why the breathers make the dominant contributions in the dynamics of a simple model of dna

influence of obstacles on the propagation speeds of nonlinear waves driven by curvature abstract we consider nonlinear waves driven by curvature in the presence of periodically distributed obstacles when the obstacles are small matano et al 2006 proved rigorously that the propagation speed of a wave mainly depends on the opening angle of the obstacles in this paper we first explain in a formal way that when the obstacles are small the propagation behavior of a wave near the obstacles has four different stages in one spatial period they can be described by traveling waves self similar solutions or curvature flows without driving force when the obstacles are large by numerical simulation we show that obstacles always decrease the propagation of waves the propagation speed is decreasing in the opening angles and the sizes of the obstacles but it is not monotone in the homogenization degree of the obstacles the periods of obstacles in a row or the isthmus widths between two rows

multibreathers in klein gordon chains with interactions beyond nearest neighbors abstract we study the existence and stability of multibreathers in klein gordon chains with interactions that are not restricted to nearest neighbors we provide a general framework where such long range effects can be taken into consideration for arbitrarily varying as a function of the node distance linear couplings between arbitrary sets of neighbors in the chain by examining special case examples such as three site breathers with next nearest neighbors we find crucial modifications to the nearest neighbor picture of one dimensional oscillators being excited either in or anti phase configurations with nontrivial phase profiles emerge from or collide with the ones with standard 0 or phase difference profiles through supercritical or subcritical bifurcations respectively similar bifurcations emerge when examining four site breathers with either next nearest neighbor or even interactions with the three nearest one dimensional neighbors the latter setting can be thought of as a prototype for the two dimensional building block namely a square of lattice nodes which is also examined

aero thermo mechanical characteristics of imperfect shape memory alloy hybrid composite panels abstract a nonlinear finite element model is provided to predict the static aero thermal deflection and the vibration behavior of geometrically imperfect shape memory alloy hybrid composite panels under the combined effect of thermal and aerodynamic loads the nonlinear governing equations are obtained using marguerre curved plate theory and the principle of virtual work taking into account the temperature dependence of material properties the effect of large deflection is included in the formulation through the von karman nonlinear strain displacement relations the thermal load is assumed to be a steady state constant temperature distribution whereas the aerodynamic pressure is modeled using the quasi steady first order piston theory the newton raphson iteration method is employed to obtain the nonlinear aero thermal deflections while an eigenvalue problem is solved at each temperature step and static aerodynamic load to predict the free vibration frequencies about the deflected equilibrium position finally the nonlinear deflection and free vibration characteristics of a composite panel are presented illustrating the effects of geometric imperfection temperature rise aerodynamic pressure boundary conditions and shape memory alloy fiber embeddings on the panel response

convergence of the cahn hilliard equation to the hele shaw model we prove that level surfaces of solutions to the cahn hilliard equation tend to solutions of the hele shaw problem under the assumption that classical solutions of the latter exist the method is based on a new matched asymptotic expansion for solutions a spectral analysis for linearizd operators and an estimate for the difference between the true solutions and certain approximate ones

existence and stability of breathers in lattices of weakly coupled two dimensional near integrable hamiltonian oscillators a method of proving the existence of breathers in lattices of two dimensional weakly coupled hamiltonian oscillators is presented this method has the advantage that provides a first approximation of the initial conditions of the breather solution together with its linear stability since the proof relies on the use of action angle variables we also present a method to perform the calculations without knowledge of the specific transformation we illustrate the results in a lattice of quartic oscillators and in another one that consists of coupled 2d morse oscillators finally we examine the possibility of extending these results in lattices of more than two degrees of freedom per lattice site

a discrete analogue of lyapunov type inequalities for nonlinear difference systems in this paper we establish several new lyapunov type inequalities for the nonlinear difference system dx n email protected n x n 1 email protected n y n m 2y n dy n email protected n x n 1 n 2x n 1 email protected n y n when the end points are not necessarily usual zeros but rather generalized zeros our results improve almost all related existing ones

nonlinear chains inside walls abstract the conservative dynamics of a 1d chain of units coupled with fpu type nonlinear interactions is considered stationary patterns in such chains emerge due to a balance of coupling energy between neighbouring units particularly interesting are the nontrivial stationary states which contain segments of positive and negative slope this results in a zig zag pattern in the case of periodic boundary conditions and in kink or anti kink solutions in the case of the free boundary conditions imposing constraints on the chain by way of two confining infinitely high walls has repercussions for the stability of these stationary states here such stationary states commensurable with the available space between the two walls are examined in detail and their respective stability properties are determined analytically by invoking the transfer matrix method strikingly stationary anti kink solutions and periodic zig zag states being unstable in the absence of confining walls become stable when confining walls are introduced furthermore simulations reveal that chains with randomly generated initial conditions can seek out these patterns thus localising energy and persist for considerable time

nonpersistence of breather families for the perturbed sine gordon equation we show that up to one exception and as a consequence of first order perturbation theory only it is impossible that a large portion of the well known family of breather solutions to the sine gordon equation could persist under any nontrivial perturbation of the form u tt u xx sin u varepsilon delta left u right o left varepsilon 2 right where is an analytic function in anarbitrarily small neighbourhood ofu 0 improving known results we analyze and overcome the particular difficulties that arise when one allows the domain of analyticity of to be small the single exception is a one dimensional linear space of perturbation functions under which the full family of breathers does persist up to first order in e

existence and stability of quasi periodic breathers in networks of ginzburg landau oscillators abstract it is shown that there is an attracting quasi periodic breather in networks of ginzburg landau oscillators

construction of quasi periodic breathers via kam technique by developing a kam theorem which involves an infinitely multiple normal frequency it is shown that there are plenty of breathers quasi periodic in time and super exponentially localized in space for the networks of weakly coupled oscillators this answers an open problem by aubry a2 in case the linearized system has no continuous spectrum

homoclinic solutions of a class of periodic difference equations with asymptotically linear nonlinearities abstract by using critical point theory and periodic approximations new sufficient conditions are obtained on the existence and nonexistence of homoclinic solutions for a class of discrete nonlinear periodic equations with asymptotically linear nonlinearities these results partially answer an open problem proposed by pankov 2006 2 under rather weaker conditions and greatly improve the related results before

exact discrete breather compactons in nonlinear klein gordon lattices we demonstrate the existence of exact discrete compact breather solutions in nonlinear klein gordon systems and complete the work of tchofo dinda and remoissenet phys rev e 60 6218 1999 by showing that the breathers stability is related principally to the lattice boundary conditions the coupling term and the harmonicity parameter

breathers in nonlinear lattices existence linear stability and quantization abstract it has been proved by the principle of anti integrable limit renamed here anti continuous limit and the implicit function theorem that under rather weak hypotheses there exist spatially localized and time periodic solutions breathers in arrays of nonlinear coupled classical oscillators provided the coupling is not too strong the models can be translationally invariant or not and be of any dimension there are also time periodic solutions corresponding to arbitrary distributions on the lattice of such solutions multibreathers the whole set of these solutions can be labeled by a discrete coding sequence the condition that the frequency of the breather or multibreather solution has no harmonics in the phonon spectrum can be discarded for a large subset of spatially extended time periodic solutions called phonobreather which correspond to special codes which can be also spatially chaotic and where no oscillator is at rest these results extend almost without change to models with coupled rotors the existence of rotobreathers which are exact solutions consisting of a single rotor rotating while the other rotors oscillate is proved there are also multirotobreather solutions and phono rotobreathers etc it is also shown that the phase of the single breathers constituting a multibreather or multirotobreather solution can be submitted to a phase torsion these new dynamical structures carry a nonzero energy flow in models with two dimensions and more the phase torsion of multibreather solutions can generate new dynamical solutions with vortices in the energy flow the dynamics of a quantum electron coupled to a classical lattice is also studied within the same approach from the anti continuous limit the existence of two kinds of polarobreathers which are spatially exponentially localized dynamical solutions is proved for a small enough electronic transfer integral the polarobreathers of the first kind include the standard static polaron the lattice configuration is static time independent when the electron is in an excited state i e the electronic oscillator oscillates periodically they can be spatially chaotic a polarobreather of the second kind corresponds to a localized periodic lattice oscillation associated with a localized quasiperiodic electronic oscillation the most simple of these solutions are those for which both the lattice oscillation and the electron wave function are mostly concentrated close to the same single site the standard floquet analysis of the linear stability of the breather and multibreather solutions is shown to be related with the band spectrum property of the newton operator involved in the implicit function theorem the krein theory of bifurcations is reinterpreted from this point of view the linear stability of the single breather and rotobreather solutions is then proved at least at small enough coupling finally it is shown that in the quantum version of translationally invariant classical models where there cannot exist in principle any strictly localized excitation there are narrow bands of excitations consisting of bound states of many bosons which are the quantum counterpart of the classical breathers the bandwidth of these excitations goes exponentially to zero with the number of bound phonons this theory provides simultaneously existence theorems and a new powerful and accurate numerical method for calculating practically any of the solutions which has been formally predicted to exist these numerical applications are currently written elsewhere

quasi periodic breathers in hamiltonian networks of long range coupling this work is concerned with hamiltonian networks of weakly and long range coupled oscillators with either variable or constant on site frequencies we derive an infinite dimensional kam like theorem by which we establish that given any n sites of the lattice there is a positive measure set of small amplitude quasi periodic breathers solutions of the hamiltonian network that are quasi periodic in time and exponentially localized in space having n frequencies which are only slightly deformed from the on site frequencies

thermal postbuckled vibrations of symmetrically laminated composite plates with initial geometric imperfections abstract in the present paper the postbuckling and postbuckled vibrations of symmetrically laminated composite plate subjected to a uniform temperature distribution through the thickness is presented the structural model is based on a higher order shear deformation theory incorporating von karman nonlinear strain displacement relations and initial geometric imperfections adopting a multi term galerkin s approximation the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations in the case of postbuckling analysis and nonlinear ordinary differential equations in the case of free vibration analysis the critical buckling temperatures are obtained from the solution of the corresponding linear eigenvalue problems postbuckled equilibrium paths are traced by solving the nonlinear algebraic equations via the newton raphson iterative procedure the free vibration frequencies of a thermally postbuckled plate are reported by solving the eigenvalue problem for different postbuckled deflections

numerical study of two dimensional disordered klein gordon lattices with cubic soft anharmonicity localized oscillations appear both in ordered nonlinear lattices breathers and in disordered linear lattices anderson modes numerical studies on a class of two dimensional systems of the klein gordon type show that there exist two different types of bifurcation in the path from nonlinearity order to linearity disorder inverse pitchforks with or without period doubling and saddle nodes this was discovered for a one dimensional system in a previous work of archilla mackay and marin the appearance of a saddle node bifurcation indicates that nonlinearity and disorder begin to interfere destructively and localization is not possible in contrast the appearance of a pitchfork bifurcation indicates that localization persists

discrete breathers localization and transfer of energy in discrete hamiltonian nonlinear systems we present a partial review of results concerning the theory of discrete breathers in nonlinear hamiltonian and discrete systems these special time periodic solutions gained much interest during the last decade because they may be involved in numerous and various phenomena in physics and biophysics where they could produce nontrivial effects of energy focusing and transfer we first review the principles which govern their existence and which are used in the existence proofs available up to now next we discuss their linear stability and the interaction of discrete breathers with small amplitude waves showing also how they could grow or decay we also briefly discuss the existence of intraband dbs in systems with a linear discrete spectrum which are not spatially periodic random or otherwise and where linear waves cannot propagate we also show that nonlinearity may restore the existence of solutions that propagate energy we review some results concerning energy transportation by dbs and especially the main features associated with their mobility we briefly discuss new perspectives opened up by the theory for applications that in particular look especially interesting for biophysics

discrete breathers classical and quantum abstract discrete breathers are time periodic spatially localised motions in networks of oscillators their occurrence in three principal contexts is reviewed i autonomous hamiltonian or reversible systems ii autonomous forced damped systems and iii time periodically forced systems the main proposed area of application however is to molecular crystals where quantum effects must be taken into account thus an idea for a theory of quantum discrete breathers is also presented though some details remain to be worked out

discrete compactons some exact results in this letter we use the method of constructing exact solutions on lattices proposed by kinnersley and described in schmidt 1979 phys rev b 20 4397 to obtain exact compacton solutions in discrete models we examine the linear stability of such solutions both for the bright compacton and for the dark compacton cases we focus on a quantization condition that the width of the profile should satisfy we also use this quantization condition to examine the possibility of compact coherent structures travelling in discrete settings our results are obtained for sinusoidal profiles and then generalized to elliptic functions of arbitrary modulus the possibility of multi compacton solutions is considered

asymptotic stability of breathers in some hamiltonian networks of weakly coupled oscillators we consider a hamiltonian chain of weakly coupled anharmonic oscillators it is well known that if the coupling is weak enough then the system admits families of periodic solutions exponentially localized in space breathers in this paper we prove asymptotic stability in energy space of such solutions the proof is based on two steps first we use canonical perturbation theory to put the system in a suitable normal form in a neighborhood of the breather second we use dispersion in order to prove asymptotic stability the main limitation of the result rests in the fact that the nonlinear part of the on site potential is required to have a zero of order 8 at the origin from a technical point of view the theory differs from that developed for hamiltonian pdes due to the fact that the breather is not a relative equilibrium of the system

compactlike discrete breathers in systems with nonlinear and nonlocal dispersive terms discrete breathers with purely anharmonic short range interaction potentials localize superexponentially becoming compactlike we analyze their spatial localization properties and their dynamical stability several branches of solutions are identified one of them connects to the well known page and sievers takeno lattice modes another one connects with the compacton solutions of rosenau the absence of linear dispersion allows for extremely long lived time quasiperiodic localized excitations adding long range anharmonic interactions leads to an extreme case of competition between length scales defining the spatial breather localization we show that short and long range interaction terms competition results in the appearance of several characteristic crossover lengths and essentially breaks the concept of compactness of the corresponding discrete breathers

nonlinear localized periodic solutions in a coupled map lattice abstract we prove the existence of nonlinear localized time periodic solutions in a chain of symplectic mappings with nearest neighbour coupling this is a class of systems whose behaviour can be seen as a representation of a lattice of pendula the effect of discrete time changes the mathematical as well as the numerical procedures applying the discrete version of floquet theory eases and clarifies the procedure of proving the existence of the localized time periodic solutions as an extension of the concept of rotobreathers one can produce solutions which rotate at every site of the lattice to consider these we use a general definition of localization

stability of discrete breathers in nonlinear klein gordon type lattices with pure anharmonic couplings we consider the discrete breathers in one dimensional nonlinear klein gordon type lattices with pure anharmonic couplings a discrete breather in the limit of vanishing couplings i e the anti continuous limit consists of a number of in phase or anti phase excited particles separated by particles at rest existence of the discrete breathers is proved for weak couplings by continuation from the anti continuous limit we prove a theorem which determines the linear stability of the discrete breathers the theorem shows that the stability or instability of a discrete breather depends on the phase difference and distance between the two sites in each pair of adjacent excited sites in the anti continuous solution it is shown that there are two types of the dependence determined by the sign of where and are parameters such that positive respectively negative represents hard respectively soft on site nonlinearity and positive respectively negative represents attractive respectively repulsive couplings

nonlinear modes in coupled rotator models abstract we compare the properties of generalized nonlinear klein gordon equations with a sinusoidal coupling sine lattice equations to those of the usual nonlinear klein gordon equation with harmonic coupling for three equations leading to the same sine gordon equation in the continuum limit using hirota s bilinear method we find a strong analogy between the properties of nonlinear oscillatory modes in the three equations numerical simulations confirm this analogy even for very discrete cases however we point out a fundamental difference between the harmonic and sinusoidal coupling by exhibiting a new class of localized nonlinear excitations which are specific to the sinusoidal coupling the rotating modes they can be created thermally an approximate analytical solution is obtained for these modes which are intrinsically discrete and appear to be extremely stable even in collisions with breathers possible implications for physics are discussed

chaotic trajectories in the standard map the concept of anti integrability a rigorous proof is given in the standard map associated with a frenkel kontorowa model for the existence of chaotic trajectories with unbounded momenta for large enough coupling constant k k0 these chaotic trajectories with finite entropy per site are coded by integer sequences mi such that the sequence bi mi 1 mi 1 2mi be bounded by some integer b the bound k0 in k depends on b and can be lowered for coding sequences mi fulfilling more restrictive conditions the obtained chaotic trajectories correspond to stationary configurations of the frenkel kontorowa model with a finite non zero photon gap called gap parameter in dimensionless units this property implies that the trajectory or the configuration ui can be uniquely continued as a uniformly continuous function of the model parameter k in some neighborhood of the initial configuration a non zero gap parameter implies that the lyapunov coefficient is strictly positive when it is defined in addition the existence of dilating and contracting manifolds is proven for these chaotic trajectories exotic trajectories such as ballistic trajectories are also proven to exist as a consequence of these theorems the concept of anti integrability emerges from these theorems in the anti integrable limit which can be only defined for a discrete time dynamical system the coordinates of the trajectory at time i do not depend on the coordinates at time i 1 thus at this singular limit the existence of chaotic trajectories is trivial and the dynamical system reduces to a bernoulli shift it is well known that the kam tori of symplectic dynamical originates by continuity from the invariant tori which exists in the integrible limit under certain conditions in a similar way it appears that the chaotic trajectories of dynamical systems originate by continuity from those which exists at the anti integrable limits also under certain conditions

on the variational structure of breather solutions i sine gordon equation abstract in this paper we describe stability properties of the sine gordon breather solution these properties are first described by suitable variational elliptic equations which also implies that the stability problem reduces in some sense to i the study of the spectrum of explicit linear systems and ii the understanding of how bad directions if any can be controlled using low regularity conservation laws then we discuss spectral properties of a fourth order linear matrix system using numerical methods we confirm that all spectral assumptions leading to the h 2 h 1 stability of sg breathers are numerically satisfied even in the ultra relativistic singular regime

generation and propagation of interfaces for reaction diffusion equations abstract this paper is concerned with the asymptotic behavior as e 0 of the solution ue of the reaction diffusion equation in r n r u t 1 2 0 where is the derivative of a bistable potential we show that if the initial data u 0 has values in both domains of attraction of the potential then an interface will develop in a short time o e 2 ln e we also show that if the wells of the potential are of equal depth then this interface will propagate with normal velocity equal to its mean curvature our result is valid as long as the interface remains smooth if the initial interface is compact and n 2 then the interface will disappear in a finite time but not if n 1 in case the depths of the wells are not equal then in order to obtain get reasonable results we must work on the scaled time s t e slower time scale in this scale we show that the interface moves with a constant speed proportional to the difference of the depths of the two wells along the normal towards the domain of the deeper well this result is valid for all s 0 and does not actually depend on the regularity of the interface we also extend the above results to the homogeneous second initial boundary value problem in case the depths of the wells are equal and the initial interface is orthogonal to the boundary we prove that the interface moves with normal velocity equal to its mean curvature provided that there is a family of hypersurfaces which moves according to their mean curvature and intersect the boundary orthogonally

targeted energy transfer between a rotor and a morse oscillator a model for selective chemical dissociation abstract standard kramers theory of chemical reactions involves a coupling with a langevin thermal bath which intrinsically forbids the possible existence of discrete breathers dbs i e local modes however it is now known that in complex systems that energy may focus for long time as discrete breathers local mode in very special systems targeted energy transfer may occur subsequently to another selected site and induces an ultraselective chemical reaction operating at low temperature the dynamics of the reaction is non brownian but highly coherent along a specific path in the phase space where the system is nearly integrable chemical expressway a simple toy model illustrating this idea is reduced to a rotor weakly coupled to a morse oscillator supposed to represent two specific local modes in a complex system which are appropriately tuned for targeted energy transfer when the rotor is initially rotating with a frequency resonant with those of the morse oscillator at rest the energy of the rotor is almost completely transferred to the morse oscillator and induces chemical dissociation the periodic oscillations of the rotor and morse oscillator remain coherent and their frequencies simultaneously vary but always remain resonant this process is analytically described within an integrable approximation numerical investigations of this model confirm that in the appropriate conditions the particle in the morse oscillator is indeed promptly ejected at infinity with a finite velocity chemical dissociation despite some chaotic transient manifesting imperfect integrability

perturbation theory for periodic orbits in a class of infinite dimensional hamiltonian systems we consider a class of hamiltonian systems describing an infinite array of coupled anharmonic oscillators and we study the bifurcation of periodic orbits off the equilibrium point the family of orbits we construct can be parametrized by their periods which belong to cantor sets of large measure containing certain periods of the linearized problem as accumulation points the infinitely many holes forming a dense set on which the existence of a periodic orbit cannot be proven originate from a dense set of resonances that are present in the system we also have a result concerning the existence of solutions of arbitrarily large amplitude

stability of discrete solitons in nonlinear schrodinger lattices we consider the discrete solitons bifurcating from the anti continuum limit of the discrete nonlinear schrodinger nls lattice the discrete soliton in the anti continuum limit represents an arbitrary finite superposition of in phase or anti phase excited nodes separated by an arbitrary sequence of empty nodes by using stability analysis we prove that the discrete solitons are all unstable near the anti continuum limit except for the solitons which consist of alternating anti phase excited nodes we classify analytically and confirm numerically the number of unstable eigenvalues associated with each family of the discrete solitons

homoclinic solutions of discrete nonlinear schrodinger equations with asymptotically or super linear terms abstract in this paper we study the following periodic discrete nonlinear schrodinger equation u n n u n n g n u n n z where the nonlinearity g n is asymptotically or super linear the sufficient conditions on the existence and on the nonexistence of nontrivial solitons was established by using critical point theory

demonstration of the stability or instability of multibreathers at low coupling abstract whereas there exists a mathematical proof for one site breathers stability and an unpublished one for two site breathers the methods for determining the stability properties of multibreathers rely on numerical computation of the floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear schrodinger equations here we present a set of multibreather stability theorems mst that provides a simple method to determine multibreathers stability in klein gordon systems these theorems are based in the application of degenerate perturbation theory to aubry s band theory we illustrate them with several examples

singular limit of a reaction diffusion equation with a spatially inhomogeneous reaction term we study reaction diffusion equations with a spatially inhomogeneous reaction term if the coefficient of these reaction term is much larger than the diffusion coefficient a sharp interface appears between two different phases we show that the equation of motion of such an interface involves a drift term despite the absence of drift in the original diffusion equations in particular we show that the same rich spatial patterns observed for a chemotaxis growth model can be realized by a system without a drift term

existence of multibreathers in chains of coupled one dimensional hamiltonian oscillators we prove the existence of monoparametric families of multibreathers in chains of hamiltonian oscillators of one degree of freedom with the total energy of the chain as a parameter at the same time we evaluate the neighborhood of the initial conditions for these solutions as well as their stability for the proof we use an idea originally proposed by poincare we apply our results to calculate families of multibreathers in a chain consisting of coupled morse oscillators

localized excitations in two dimensional hamiltonian lattices we analyze the origin and features of localized excitations in a discrete two dimensional hamiltonian lattice the lattice obeys discrete translational symmetry and the localized excitations exist because of the presence of nonlinearities we connect the presence of these excitations with the existence of local integrability of the original n degree of freedom system on the basis of this explanation we make several predictions about the existence and stability of these excitations this work is an extension of previously published results on vibrational localization in one dimensional nonlinear hamiltonian lattices phys rev e 49 1994 836 thus we confirm earlier suggestions about the generic property of hamiltonian lattices to exhibit localized excitations independent on the dimensionality of the lattice

imperfection sensitivity in the nonlinear vibration oscillations of initially stressed plates abstract in this paper nonlinear partial differential equations for the vibrating motion of an initially stressed imperfect isotropic plate are presented the derived equations include the effects for imperfections transverse shear deformation rotary inertia and non uniform initial stresses using these derived governing equations the nonlinear vibration of initially stressed plates with initial imperfection is studied present approach employs perturbation technique galerkin method and runge kutta method the perturbation technique was used to derive the nonlinear governing equations the motion of imperfect plates is obtained by performing the galerkin method and then solved by runge kutta method numerical solutions are presented that relate to the performances of perfect and imperfect plates a combination of pure bending stress plus an extensional stress is taken to be the initial stress in the plane of the plate it is found that the existence of initial stresses and geometric imperfection may result in a drastic change on the nonlinear vibration behavior the effects of various parameters on the nonlinear free vibrations of imperfect plates are presented

on a class of discretizations of hamiltonian nonlinear partial differential equations abstract we present a new class of discretizations of partial differential equations pdes that preserve a momentum like integral of the motion this results in an effective translational invariance for the dynamical problem and the absence of a peierls nabarro barrier that is usually present in discretizations of hamiltonian pdes a general method to construct such discretizations for any nonlinearity is given and the properties of the resulting differential difference equations are analyzed in a number of different cases for nonlinear klein gordon as well for nonlinear schrodinger type systems while for the former nonintegrability of the dynamical problem is evident in the latter case numerical evidence suggests that the behavior is close to the one of integrable systems we also show how static solutions of the equations can be constructed for these discretizations and discuss the similarities and differences of the method with previously reported ones

discrete nonlinear schrodinger equations with superlinear nonlinearities abstract in this paper we study the discrete nonlinear equation lu n u n n g n u n n z where belongs to a finite spectral gap of the operator l or it is a lower edge of a finite spectral gap by using a variant generalized weak linking theorem for strongly indefinite problem developed by schechter and zou we will study the existence of nontrivial solitons for this equation with gn is super linear

global existence and compact attractors for the discrete nonlinear schrodinger equation abstract we study the asymptotic behavior of solutions of discrete nonlinear schrodinger type dnls equations for a conservative system we consider the global in time solvability and the question of existence of standing wave solutions similarities and differences with the continuous counterpart nls partial differential equation are pointed out for a dissipative system we prove existence of a global attractor and its stability under finite dimensional approximations similar questions are treated in a weighted phase space finally we propose possible extensions for various types of dnls equations

multistable solitons in the cubic quintic discrete nonlinear schrodinger equation we analyze the existence and stability of localized solutions in the one dimensional discrete nonlinear schrodinger dnls equation with a combination of competing self focusing cubic and defocusing quintic onsite nonlinearities we produce a stability diagram for different families of soliton solutions that suggests the co existence of infinitely many branches of stable localized solutions bifurcations that occur with an increase in the coupling constant are studied in a numerical form a variational approximation is developed for accurate prediction of the most fundamental and next order solitons together with their bifurcations salient properties of the model which distinguish it from the well known cubic dnls equation are the existence of two different types of symmetric solitons and stable asymmetric soliton solutions that are found in narrow regions of the parameter space the asymmetric solutions appear from and disappear back into the symmetric ones via loops of forward and backward pitchfork bifurcations

discrete breathers in vibroimpact chains analytic solutions we present exact analytic solutions for discrete breathers in essentially nonlinear oscillatory chains belonging to both of the most common universality classes klein gordon and fermi pasta ulam the exact solutions can be obtained due to use of vibroimpact potentials combining extreme nonlinearity with the possibility of description in terms of a forced linear model under conditions of self consistency a crossover between the cases of high and low energies can be studied directly the solutions obtained may be used as a high energy limit for models with other realistic potentials as well as benchmarks for the testing of approximate approaches in the theory of discrete breathers

conditions on the existence of localized excitations in nonlinear discrete systems we use recent results that localized excitations in nonlinear hamiltonian lattices can be viewed and described as multiple frequency excitations their dynamics in phase space takes place on tori of corresponding dimension for a one dimensional hamiltonian lattice with nearest neighbour interaction we transform the problem of solving the coupled differential equations of motion into a certain mapping m l 1 f m l m l 1 where m l for every l lattice site is a function defined on an infinite discrete space of the same dimension as the torus we consider this mapping in the tails of the localized excitation i e for l rightarrow pm infty for a generic hamiltonian lattice the thus linearized mapping is analyzed we find conditions of existence of periodic one frequency localized excitations as well as of multiple frequency excitations the symmetries of the solutions are obtained as a result we find that the existence of localized excitations can be a generic property of nonlinear hamiltonian lattices in contrast to nonlinear hamiltonian fields

effective hamiltonian for travelling discrete breathers hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers however solutions which look like moving discrete breathers for some time are not difficult to observe in numerics in this paper we propose an abstract framework for the description of approximate travelling discrete breathers in hamiltonian chains of oscillators the method is based on the construction of an effective hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers error estimate on the approximate dynamics is also studied the concept of the peierls nabarro barrier can be made clear in this framework we illustrate the method with two simple examples namely the salerno model which interpolates between the ablowitz ladik lattice and the discrete nonlinear schrodinger system and the fermi pasta ulam chain

equivalence of uniform hyperbolicity for symplectic twist maps and phonon gap for frenkel kontorova models there is a well known correspondence between the dynamics of symplectic twist maps which represent an important class of hamiltonian systems and the equilibrium states of a class of variational problems in solid state physics known as frenkel kontorova models in this paper it is shown that the key concepts of uniform hyperbolicity in the first context and phonon gap in the second context are equivalent this allows one to transfer many ideas between the two and hence to deduce new results for example we prove the uniform hyperbolicity of certain invariant sets for symplectic twist maps constructed from so called non degenerate anti integrable limits by aubry and abramovici using the concept of phonon gap and deduce that they have measure zero we prove existence of many multi defect equilibrium states for a frenkel kontorova system if it has a single non degenerate defect equilibrium state via standard results in the theory of uniform hyperbolicity

supratransmission in a disordered nonlinear periodic structure abstract we study the interaction among dispersion nonlinearity and disorder effects in the context of wave transmission through a discrete periodic structure subjected to continuous harmonic excitation in its stop band we consider a damped nonlinear periodic structure of finite length with disorder disorder is introduced throughout the structure by small changes in the stiffness parameters drawn from a uniform statistical distribution dispersion effects forbid wave transmission within the stop band of the linear periodic structure however nonlinearity leads to supratransmission phenomenon by which enhanced wave transmission occurs within the stop band of the periodic structure when forced at an amplitude exceeding a certain threshold the frequency components of the transmitted waves lie within the pass band of the linear structure where disorder is known to cause anderson localization there is therefore a competition between dispersion nonlinearity and disorder in the context of supratransmission we show that supratransmission persists in the presence of disorder the influence of disorder decreases in general as the forcing frequency moves away from the pass band edge reminiscent of dispersion effects subsuming disorder effects in linear periodic structures we compute the dependence of the supratransmission force threshold on nonlinearity and strength of coupling between units we observe that nonlinear forces are confined to the driven unit for weakly coupled systems this observation together with the truncation of higher order nonlinear terms permits us to develop closed form expressions for the supratransmission force threshold in sum in the frequency range studied here disorder does not influence the supratransmission force threshold in the ensemble average sense but it does reduce the average transmitted wave energy

lyapunov inequalities and stability for discrete linear hamiltonian systems abstract in this paper we establish several new lyapunov type inequalities for discrete linear hamiltonian systems when the end points are not necessarily usual zeros but rather generalized zeros which generalize and improve almost all related existing ones applying these inequalities an optimal stability criterion is obtained

large memory capacity in chaotic artificial neural networks a view of the anti integrable limit in the literature it was reported that the chaotic artificial neural network model with sinusoidal activation functions possesses a large memory capacity as well as a remarkable ability of retrieving the stored patterns better than the conventional chaotic model with only monotonic activation functions such as sigmoidal functions this paper from the viewpoint of the anti integrable limit elucidates the mechanism inducing the superiority of the model with periodic activation functions that includes sinusoidal functions particularly by virtue of the anti integrable limit technique this paper shows that any finite dimensional neural network model with periodic activation functions and properly selected parameters has much more abundant chaotic dynamics that truly determine the model s memory capacity and pattern retrieval ability to some extent this paper mathematically and numerically demonstrates that an appropriate choice of the activation functions and control scheme can lead to a large memory capacity and better pattern retrieval ability of the artificial neural network models

breathers on diatomic fermi pasta ulam lattices we prove the existence of breathers spatially localized and time periodic oscillations in diatomic fermi pasta ulam fpu chains with arbitrary mass ratio this completes an existence result by livi spicci and mackay valid for large mass ratio the problem is formulated as a mapping in a loop space and analyzed via a discrete spatial centre manifold reduction plane wave solutions of the linearized system have frequencies in a higher optic band or a lower acoustic band for frequencies close to band edges all small amplitude solutions of the nonlinear system lie on a finite dimensional centre manifold which reduces the problem locally to the study of a finite dimensional mapping for good parameter values the map admits homoclinic orbits to 0 corresponding to discrete breathers when the fpu interaction potential satisfies a hardening condition we find breathers with frequencies slightly above the optic band or in the gap slightly above the acoustic band for a potential satisfying the opposite softening condition we obtain breathers with frequencies in the gap slightly below the optic band 2004 elsevier b v all rights reserved

singular limits of spatially inhomogeneous convection reaction diffusion equations we study convection reaction diffusion equations which have spatially inhomogeneous steady states when the coefficients of the reaction terms are much larger than the diffusion coefficients sharp interfaces appear between two stable inhomogeneous steady states by using the method of matched asymptotic expansions we derive the equations of the motion of such interfaces which depend on the mean curvature of the interfaces and depend on the inhomogeneous coefficients locally

obtaining breathers in nonlinear hamiltonian lattices we present a numerical method for obtaining high accuracy numerical solutions of spatially localized time periodic excitations on a nonlinear hamiltonian lattice we compare these results with analytical considerations of the spatial decay we show that nonlinear contributions have to be considered and we obtain very good agreement between the latter and numerical results we discuss further applications of the method and results

lower and upper estimates on the excitation threshold for breathers in discrete nonlinear schrodinger lattices we propose analytical lower and upper estimates on the excitation threshold for breathers in the form of spatially localized and time periodic solutions in discrete nonlinear schrodinger dnls lattices with power nonlinearity the estimation depending explicitly on the lattice parameters is derived by a combination of a comparison argument on appropriate lower bounds depending on the frequency of each solution with a simple and justified heuristic argument the numerical studies verify that the analytical estimates can be of particular usefulness as a simple analytical detection of the activation energy for breathers in dnls lattices

standing waves for discrete schrodinger equations in infinite lattices with saturable nonlinearities abstract in this paper we consider the periodic discrete nonlinear equation l u n u n g n u n n z lim n u n 0 where l is a jacobi operator and the nonlinearities g n s are asymptotically linear as s in the two different cases is a spectral endpoint of l or it belongs to a finite spectral gap of l we obtain the existence of nontrivial solitons of this equation by using variational methods in particular a necessary and sufficient condition is obtained for the existence of gap solitons of the nonlinear equation here solitons appear when we look for standing waves of some discrete nonlinear schrodinger equations

properties of one dimensional anharmonic lattice solitons abstract the existence of bell and kink shaped solitons moving at constant velocity while keeping a permanent profile is studied in infinite periodic monoatomic chains of arbitrary anharmonicity by taking advantage of the equation of motion being integrable with respect to solitons a second order non linear differential equation involving advanced and retarded terms must be solved which is done by implementing a scheme based on the finite element and newton s methods if the potential has a harmonic limit the asymptotic time decay behaves exponentially and there is a dispersion relation between propagation velocity and decay time inversely if the potential has no harmonic limit the asymptotic regime shows up either as a power law or faster than exponential excellent agreement is achieved with toda s model illustrative examples are also given for the fermi pasta ulam and sine gordon potentials owing to integrability an effective one body potential is worked out in each case lattice and continuum solitons differ markedly from one another as regards the amplitude versus propagation velocity relationship and the asymptotic time behavior the relevance of the linear stability analysis when applied to solitons propagating in an infinite crystal is questioned the reasons preventing solitons from arising in a diatomic lattice are discussed

discrete breathers on symmetry determined invariant manifolds for scalar models on the plane square lattice a group theoretical approach for studying localized periodic and quasiperiodic vibrations in two and three dimensional lattice dynamical models is developed this approach is demonstrated for the scalar models on the plane square lattice the symmetry determined invariant manifolds admitting existence of localized vibrations are found and some types of discrete breathers are constructed on these manifolds a general method using the apparatus of matrix representations of symmetry groups to simplify the standard linear stability analysis is discussed this method allows one to decompose the corresponding system of linear differential equations with time dependent coefficients into a number of independent subsystems whose dimensions are less than the full dimension of the considered system

discrete breathers in disordered media abstract we describe some simple physical models where discrete breathers nonlinear localised modes in a lattice exist together with spatial disorder as the models are translation invariant both spatial localisation and spatial disorder are only due to the interplay of nonlinearity and discreteness this result is obtained as a straightforward application of a general result of existence of discrete breathers j a sepulchre r s mackay localised oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators nonlinearity 10 1997 1 35

finite size effects on instabilities of discrete breathers abstract when the two arcs of the continuous phonon spectrum of the floquet matrix of a discrete breather overlap on the unit circle the breather solution in the infinite lattice might be stable while the corresponding solutions in finite systems appear to be unstable more precisely when the model parameters vary the breather in the finite system exhibits a large number of collisions between the floquet eigenvalues belonging to the phonon spectrum these collisions correspond to complex cascades of instability thresholds followed near after by re entrant stability thresholds we interpret this complex structure on the basis of the band analysis of the matrix of the second variation of the action then we can predict that in the limit of an infinite system the number of instability and stability thresholds in the cascade diverges but simultaneously the maximum amplitude of the instabilities vanishes so that the breather in the infinite system recovers its linear stability as long as all its other localized modes remain stable this is the situation which is required in cretegny et al physica d 119 1998 73 87 for having inelastic phonon scattering with two channels we also analyze the size effects when a floquet eigenvalue associated with a localized mode collides with the floquet continuous phonon spectrum with different krein signature in contrast to the previous case the infinite system is unstable after the collision

solitons in one dimensional nonlinear schrodinger lattices with a local inhomogeneity in this paper we analyze the existence stability dynamical formation and mobility properties of localized solutions in a one dimensional system described by the discrete nonlinear schrodinger equation with a linear point defect we consider both attractive and repulsive defects in a focusing lattice among our main findings are a the destabilization of the on site mode centered at the defect in the repulsive case b the disappearance of localized modes in the vicinity of the defect due to saddle node bifurcations for sufficiently strong defects of either type c the decrease of the amplitude formation threshold for attractive and its increase for repulsive defects and d the detailed elucidation as a function of initial speed and defect strength of the different regimes trapping trapping and reflection pure reflection and pure transmission of interaction of a moving localized mode with the defect

anti integrability in dynamic and variational problems abstract we show using a series of examples that the existence of a singular limit called anti integrable can be useful for proving the existence of chaotic solutions and elucidating some of their properties leading to some new and unexpected results in particular the existence proof of chaotic trajectories in large classes of dynamical systems with discrete time becomes straightforward the method applies even for maps in infinite dimension symplectic or not similar ideas can be used for proving the existence of breathers or self localised modes and of chaotic distributions of breathers in any array of weakly coupled non linear oscillators with continuous time the existence of insulating bipolaronic structures in electron phonon systems electronic self localisation at large electron phonon coupling can also be proven on the same basis

continuation of periodic orbits in conservative and hamiltonian systems we introduce and justify a computational scheme for the continuation of periodic orbits in systems with one or more first integrals and in particular in hamiltonian systems having several independent symmetries our method is based on a generalization of the concept of a normal periodic orbit as introduced by sepulchre and mackay nonlinearity 10 1997 679 we illustrate the continuation method on some integrable hamiltonian systems with two degrees of freedom and briefly discuss some further applications

discrete gap breathers in a diatomic klein gordon chain stability and mobility a one dimensional diatomic chain with harmonic intersite potential and nonlinear external potential is considered the klein gordon model localized solutions of the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum gap breathers are studied numerically the linear stability analysis for these solutions is performed while changing the system parameters from the anticontinuous to the continuous limit two different types of solutions are considered symmetric centered at a heavy atom and antisymmetric centered at a light atom respectively different mechanisms of instability oscillatory as well as nonoscillatory of the gap breathers are studied and the influence of the instabilities on the breather solutions is investigated in the dynamics simulations in particular the presence of an inversion of stability regime with simultaneous nonoscillatory instabilities of symmetric and antisymmetric solutions with respect to antisymmetric perturbations is found yielding practically radiationless mobility