configurational invariants of hamiltonian systems in this paper we explore the general conditions in order that a two dimensional natural hamiltonian system possess a second invariant which is a polynomial in the momenta and is therefore liouville integrable we examine the possibility that the invariant is preserved by the hamiltonian flow on a given energy hypersurface only weak integrability and derive the additional requirement necessary to have conservation at arbitrary energy strong integrability using null complex coordinates we show that the leading order coefficient of the polynomial is an arbitrary holomorphic function in the case of weak integrability and a polynomial in the coordinates in the strongly integrable one we review the results obtained so far with strong invariants up to degree four and provide some new examples of weakly integrable systems with linear and quadratic invariants

moment estimate and existence for solutions of stochastic functional differential equations abstract in this paper we give the existence uniqueness theorems and the moment estimates of solutions for a large class of sfdes these estimates improve and extend some related results including exponential stability decay stability and asymptotic behavior their corollaries improve and extend the classical halanay inequality and some of its generalizations moreover the stochastic version of the wintner theorem in continuous function space is established by the compare principle which improves and extends the main results of xu et al 2008 2013 when the methods presented are applied to the sfdes with impulses and sfdes in hilbert spaces we extend the related results of govindan and ahmed 2013 liu et al 2007 2010 vinodkumar 2010 and xu et al 2012 two examples are provided to illustrate the effectiveness of our results

topological gauge theories and group cohomology we show that three dimensional chern simons gauge theories with a compact gauge groupg not necessarily connected or simply connected can be classified by the integer cohomology grouph4 bg z in a similar way possible wess zumino interactions of such a groupg are classified byh3 g z the relation between three dimensional chern simons gauge theory and two dimensional sigma models involves a certain natural map fromh4 bg z toh3 g z we generalize this correspondence to topological spin theories which are defined on three manifolds with spin structure and are related to what might be calledz2 graded chiral algebras or chiral superalgebras in two dimensions finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group establishing links with two dimensional holomorphic orbifold models

rigorous results for the minimal speed of kolmogorov petrovskii piscounov monotonic fronts with a cutoffa we study the effect of a cutoff on the speed of pulled fronts of the one dimensional reaction diffusion equation to accomplish this we first use variational techniques to prove the existence of a heteroclinic orbit in phase space for traveling wave solutions of the corresponding reaction diffusion equation under conditions that include discontinuous reaction profiles this existence result allows us to prove rigorous upper and lower bounds on the minimal speed of monotonic fronts in terms of the cut off parameter from these bounds we estimate the range of validity of the brunet derrida formula for a general class of reaction terms

on quantum gauge theories in two dimensions two dimensional quantum yang mills theory is studied from three points of view i by standard physical methods ii by relating it to the largek limit of three dimensional chern simons theory and two dimensional conformal field theory iii by relating its weak coupling limit to the theory of reidemeister ray singer torsion the results obtained from the three points of view agree and give formulas for the volumes of the moduli spaces of representations of fundamental groups of two dimensional surfaces

integrable hamiltonian systems with vector potentials we investigate integrable two dimensional hamiltonian systems with scalar and vector potentials admitting second invariants which are linear or quadratic in the momenta in the case of a linear second invariant we provide some examples of weakly integrable systems in the case of a quadratic second invariant we recover the classical strongly integrable systems in cartesian and polar coordinates and provide some new examples of integrable systems in parabolic and elliptical coordinates

topological models on the lattice and a remark on string theory cloning the addition of a topological model to the matter content of a conventional closed string theory leads to the appearance of many perturbatively decoupled spacetime worlds we illustrate this by classifying topological vertex models on a triangulated surface we comment on how such worlds could have been coupled in the planck era

pattern propagation in nonlinear dissipative systems abstract we discuss the problem of pattern selection in situations where a stable nonuniform state of a nonlinear dissipative system propagates into an initially unstable homogeneous region our strategy is to consider this process as a generalization of front propagation in a nonlinear diffusion problem for which rigorous results are known and we point out that these known properties are consistent with a marginal stability hypothesis that has been suggested in the theory of dendritic crystal growth we then describe a more general interpretation of the marginal stability hypothesis and finally present numerical evidence for its validity from three different pattern forming models

impulsive effects on stability of cohen grossberg neural networks with variable delays in this paper a model of impulsive cohen grossberg neural networks is first formulated by establishing some impulsive differential inequalities we investigate impulsive effects on the stability of cohen grossberg neural networks with variable delays and obtain some sufficient conditions ensuring global exponential stability of the impulsive delay system our criteria not only show that the stability still remains under certain impulsive perturbations for some continuous stable neural networks but also present an approach to stabilize the unstable neural networks by utilizing impulsive effects the results extend and improve some recent works for impulsive neural networks as well as non impulsive neural networks some examples and their simulations are given for illustration of the theoretical results

lattice topological field theory in two dimensions the lattice definition of a two dimensional topological field theory tft is given generically and the exact solution is obtained explicitly in particular the set of all lattice topological field theories is shown to be in one to one correspondence with the set of all associative algebrasr and the physical hilbert space is identified with the centerz r of the associative algebrar perturbations of tft s are also considered in this approach showing that the form of topological perturbations is automatically determined and that all tft s are obtained from one tft by such perturbations several examples are presented including twistedn 2 minimal topological matter and the case wherer is a group ring

on the decomposition of tensor products of the representations of the classical groups by means of the universal characters on definit les caracteres universels d une representation rationnelle de gl n c et on donne les formules de decomposition des produits tensoriels entre eux en termes de coefficients de littlewood richardson on demontre les formules de decomposition du produit tensoriel de deux representations irreductibles de sp 2n c et de so n c

multi matrix models and noncommutative frobenius algebras obtained from symmetric groups and brauer algebras it has been understood that correlation functions of multi trace operators in mathcal n 4 sym can be neatly computed using the group algebra of symmetric groups or walled brauer algebras on the other hand such algebras have been known to construct 2d topological field theories tfts after reviewing the construction of 2d tfts based on symmetric groups we construct 2d tfts based on walled brauer algebras in the construction the introduction of a dual basis manifests a similarity between the two theories we next construct a class of 2d field theories whose physical operators have the same symmetry as multi trace operators constructed from some matrices such field theories correspond to non commutative frobenius algebras a matrix structure arises as a consequence of the noncommutativity correlation functions of the gaussian complex multi matrix models can be translated into correlation functions of the two dimensional field theories

pattern selection in long wavelength convection abstract the long wavelength of the first instability in rayleigh benard convection between nearly thermally insulating horizontal plates is typical of a variety of physical systems the evolution of such an instability is described by the equation t 2 4 2 2 2 2 where is the planform function is the scaled rayleigh number and 1 the quantities represent the effects of finite biot number asymmetry in the boundary conditions at top and bottom and departures from the boussinesq approximation respectively the quantity when the original problem is self adjoint but otherwise planform selection is studied for 1 using equivariant bifurcation theory on the square lattice both rolls and squares can be stable depending on the parameters and the possible secondary bifurcations located near various codimension two singularities are analyzed on the hexagonal lattice the primary bifurcation is always degenerate when 0 of the six primary solution branches possible in this case the hexagon branch is stable when 0 both rolls and hexagons bifurcate supercritically but rolls are stable finally when and or 0 a hysteretic transition to h or h occurs depending on sgn k 2 c if stable h h coexist at larger amplitudes but if k 2 c 0 1 a further hysteretic transition takes place with increasing amplitude in which the hexagons are replaced by stable rolls

order parameter equations for long wavelength instabilities abstract we consider order parameter equations describing the nonlinear evolution of finite amplitude disturbances near the threshold of a large scale instability it is shown that the ginzburg landau equation is not valid in many cases the structure of typical order parameter equations is discussed

mean square exponential stability of stochastic recurrent neural networks with time varying delays the stability of a class of stochastic recurrent neural networks with time varying delays is investigated in this paper with the help of the lyapunov function and the dini derivative of the expectation of v t x t along the solution x t of the model a set of novel sufficient conditions on mean square exponential stability has been established an example is also given to illustrate the effectiveness of our results

nonlinear aspects of the cahn hilliard equation abstract this paper treats phase separation within the context of the phenomenological cahn hilliard equation c t m c f c k 2 c where c is the concentration m c is the mobility and f c is homogeneou s free energy which is assumed here to be a fourth degree polynomial natural boundary conditions are introduced the full set of equilibrium solutions is specified a comparison theorem for stability criteria which was postulated by langer is proved here within the framework of the natural boundary conditions energy methods are used to define and estimate the limit of monotonic global stability it is pointed out that within the parameter region where the uniform homogeneous state is the only equilibrium solution there may still exist some internal excitable region in which the homogeneous solution possesses growing fluctuations furthermore a periodic instability is shown to exist in the metastable region in addition to the well known nucleation instability

pth moment stability analysis of stochastic recurrent neural networks with time varying delays this paper addresses in great detail the issue of pth moment exponential stability of stochastic recurrent neural networks with time varying delays with the help of the dini derivative of the expectation of v t x t along the solution x t of the model and the technique of halanay type inequality some novel sufficient conditions on pth moment exponential stability of the trivial solution has been established results of the development as presented in this paper are more general than those reported in some previously published papers an example is also given to illustrate that our results are correct and effectiveness

slowly oscillating wave solutions of a single species reaction diffusion equation with delay we study positive bounded wave solutions u t x x ct 0 of equation ut t x u t x u t x g u t h x x rm this equation is assumed to have two non negative equilibria u1 0 and u2 0 the birth function g c r r is unimodal and differentiable at 0 and some results also require the feedback condition g s s c our results are based on a detailed geometric description of the wave profile in particular the monotonicity of its leading edge is established we also discuss the uniqueness problem indicating a subclass g of asymmetric tent maps such that given g g there exists exactly one positive travelling front for each fixed admissible speed

speed selection for traveling wave solutions to the diffusion reaction equation with cubic reaction term and burgers nonlinear convection the problem of traveling wave tw speed selection for solutions to a generalized murray burgers kpp fisher parabolic equation with a strictly positive cubic reaction term is considered theoretically and the initial boundary value problem is numerically solved in order to support obtained analytical results depending on the magnitude of a parameter inherent in the reaction term i the term is either a concave function or a function with the inflection point and ii transition from pulled to pushed tw solution occurs due to interplay of two nonlinear terms the reaction term and the burgers convection term explicit pushed tw solutions are derived it is shown that physically observable tw solutions i e solutions obtained by solving the initial boundary value problem with a sufficiently steep initial condition can be determined by seeking the tw solution characterized by the maximum decay rate at its leading edge in the appendix the developed approach is applied to a non linear diffusion reaction equation that is widely used to model premixed turbulent combustion

stability analysis in lagrange sense for a non autonomous cohen grossberg neural network with mixed delays abstract the paper discusses the global exponential stability in the lagrange sense for a non autonomous cohen grossberg neural network cgnn with time varying and distributed delays the boundedness and global exponential attractivity of non autonomous cgnn with time varying and distributed delays are investigated by constructing appropriate lyapunov like functions moreover we provide verifiable criteria on the basis of considering three different types of activation function which include both bounded and unbounded activation functions these results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria meanwhile the results obtained in this paper are more general and challenging than that of the existing references in the end an illustrative example is given to verify our results

convergence dynamics of stochastic cohen grossberg neural networks with unbounded distributed delays this paper addresses the issue of the convergence dynamics of stochastic cohen grossberg neural networks scgnns with white noise whose state variables are described by stochastic nonlinear integro differential equations with the help of lyapunov functional semi martingale theory and inequality techniques some novel sufficient conditions on pth moment exponential stability and almost sure exponential stability for scgnn are given furthermore as byproducts of our main results some sufficient conditions for checking stability of deterministic cgnns with unbounded distributed delays have been established especially even when the spectral radius of the coefficient matrix is greater than 1 in some cases our theory is also effective

variational approach to a class of nonlinear oscillators with several limit cycles we study limit cycles of nonlinear oscillators described by the equation x nuf x x 0 with f an odd function depending on the nonlinearity this equation may exhibit one or more limit cycles we show that limit cycles correspond to relative extrema of a certain functional analytical results in the limits nu 0 and nu infinity are in agreement with previously known criteria for intermediate nu numerical determination of the limit cycles can be obtained

stability analysis of impulsive stochastic cohen grossberg neural networks driven by g brownian motion this paper is devoted to study the stability of a class of impulsive stochastic cohen grossberg neural networks driven by g brownian motion by means of g lyapunov function borel cantelli lemma an

exact fronts for the nonlinear diffusion equation with quintic nonlinearities we consider travelling wave solutions of the reaction diffusion equation with quintic nonlinearities u t u xx mu u 1 u 1 alpha u beta u 2 gamma u 3 if the parameters alpha beta and gamma obey a special relation then the criterion for the existence of a strong heteroclinic connection can be expressed in terms of two of these parameters if an additional restriction is imposed explicit front solutions can be obtained the approach used can be extended to polynomials whose highest degree is odd

global feedback control for pattern forming systems global feedback control of pattern formation in a wide class of systems described by the swift hohenberg sh equation is investigated theoretically by means of stability analysis and numerical simulations two cases are considered i feedback control of the competition between hexagon and roll patterns described by a supercritical sh equation and ii the use of feedback control to suppress the blowup in a system described by a subcritical sh equation in case i it is shown that feedback control can change the hexagon and roll stability regions in the parameter space as well as cause a transition from up to down hexagons and stabilize a skewed mixed mode hexagonal pattern in case ii it is demonstrated that feedback control can suppress blowup and lead to the formation of spatially localized patterns in the weakly nonlinear regime the effects of a delayed feedback are also investigated for both cases and it is shown that delay can induce temporal oscillations as well as blowup

on the transition from pulled to pushed monotonic fronts of the extended fisher kolmogorov equation abstract the extended fisher kolmogorov equation u t u xx u xxxx f u with arbitrary positive f u satisfying f 0 f 1 0 has monotonic traveling fronts for 1 12 we find a simple lower bound on the speed of the fronts which allows to determine for a given reaction term when will the front of minimal speed be pushed

tensor product representations of general linear groups and their connections with brauer algebras abstract for the complex general linear group g gl r c we investigate the tensor product module t p v q v of p copies of its natural representation v c r and q copies of the dual spare v of v we describe the maximal vectors of t and from that obtain an explicit decomposition of t into its irreducible g summands knowledge of the maximal vectors allows us to determine the centralizer algebra c of all transformations on t commuting with the action of g to construct the irreducible c representations and to identify c with a certain subalgebra b r p q of the brauer algebra b r p q

hierarchy of bifurcations of space periodic structures in a nonlinear model of active dissipative media abstract this work is a detailed research of spatial periodic structures and their bifurcations in a nonlinear model of media with an active dissipation presented here is an obvious bifurcation diagram of stationary solutions attractors on a wide scale of wave numbers are studied and classified significant progress in understanding of behavior of nonstationary solutions is attained

dynamic analysis of stochastic cohen grossberg neural networks with time delays abstract in this paper we discuss stochastic cohen grossberg neural networks with time delays by constructing suitable lyapunov functional and employing the semimartingale convergence theorem we give some sufficient criteria ensuring almost sure exponential stability of the networks the results obtained are helpful to design stability of networks when stochastic noise is taken into consideration

singularities in a modified kuramoto sivashinsky equation describing interface motion for phase transition abstract phase transitions can be modeled by the motion of an interface between two locally stable phases a modified kuramoto sivashinsky equation h t 2 h 4 h 1 h 2 2 h 2 h xx h yy h xy 2 describes near planar interfaces which are marginally long wave unstable we study the question of finite time singularity formation in this equation in one and two space dimensions on a periodic domain such singularity formation does not occur in the kuramoto sivashinsky equation 0 for all 1 0 we provide sufficient conditions on the initial data and size of the domain to guarantee a finite time blow up in which a second derivative of h becomes unbounded using a bifurcation theory analysis we show a parallel between the stability of steady periodic solutions and the question of finite time blow up in one dimension finally we consider the local structure of the blow up in the one dimensional case via similarity solutions and numerical simulations that employ a dynamically adaptive self similar grid the simulations resolve the singularity to over 25 decades in h xx l and indicate that the singularities are all locally described by a unique self similar profile in h xx we discuss the relevance of these observations to the full intrinsic equations of motion and the associated physics

stability in delayed cohen grossberg neural networks lmi optimization approach in this paper stability problems are further discussed for a class of delayed cohen grossberg neural networks on the basis of the linear matrix inequality lmi optimization approach and also the lyapunov krasovskii functional method combined with the halanay inequality technique several new sufficient criteria are given for ascertaining the global asymptotic stability and exponential stability of the equilibrium point for this system the proposed results are less restrictive than those given in the earlier literature and are easier to verify in practice in addition four examples and their numerical simulations are given two of them are used to demonstrate the effectiveness of the proposed results and another two show that there exist stable bifurcating periodic solutions if the given conditions do not hold

boundedness and stability for cohen grossberg neural network with time varying delays abstract in this paper a model is considered to describe the dynamics of cohen grossberg neural network with variable coefficients and time varying delays uniformly ultimate boundedness and uniform boundedness are studied for the model by utilizing the hardy inequality combining with the halanay inequality and the lyapunov functional method some new sufficient conditions are derived for the model to be globally exponentially stable the activation functions are not assumed to be differentiable or strictly increasing moreover no assumption on the symmetry of the connection matrices is necessary these criteria are important in signal processing and the design of networks

large amplitude solutions to the sivashinsky and riley davis equations for directional solidification abstract directional solidification of a dilute binary alloy is often characterized by the appearance of deep root finger type interfaces as a model of this phenomenon we investigate the large amplitude behavior of long wave evolution equations previously derived for directional solidification in this paper we conduct a detailed asymptotic and numerical study of the periodic solutions of the sivashinsky and riley davis equations the sivashinsky equation which describes the limit of small segregation coefficient is shown to form deep root solutions which can be described in terms of elliptic functions however this equation is known to be ill posed in the sense that the solution branches are unstable and large classes of initial conditions lead to finite time blow up by considering asymptotically large surface energy riley and davis derived an evolution equation which may be considered a regularizing perturbation of the sivashinsky equation this equation has steady large amplitude solutions which are linearly stable in the absence of solutal segregation we may describe these solutions asymptotically in this limit amplitudes and wavelengths may become arbitrarily large a stability analysis suggests that with periodic boundary conditions the solution may coarsen until a single finger fills the domain if segregation effects are included both the amplitude and wavelength are bounded independent of domain size this wavelength bound gives the system a finger width selection mechanism associated with a tip splitting bifurcation that has also been observed in experiments

state estimation for neural networks of neutral type with interval time varying delays in this paper the design problem of state estimator for a class of neural networks of neutral type with interval time varying delays is studied the interval time varying delay does not have constraint that its derivative is less than 1 the constraint is widely used to deal with time varying delays in many papers a delay dependent linear matrix inequality lmi criterion for existence of the estimator is proposed by using lyapunov method the criterion can be easily solved by various convex optimization algorithms a numerical example is given to show the effectiveness of proposed method

large n 2d yang mills theory and topological string theory we describe a topological string theory which reproduces many aspects of the 1 n expansion of su n yang mills theory in two spacetime dimensions in the zero coupling a 0 limit the string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target the derivation of the string theory relies on a new interpretation of gross and taylor s 1 points we describe how inclusion of the area coupling of chiral sectors and wilson loop expectation values can be incorporated in the topological string approach

bifurcation analysis of cellular interfaces in unidirectional solidification of a dilute binary mixture analytical bifurcation theory is used to study interface patterns in the unidirectional solidification of a dilute binary mixture armbruster and dangelmayr s classification of bifurcation equations equivariant under the diagonal action in mathbb c 2 of the symmetry group o 2 is used to show that the local bifurcation structure of the model long wave evolution equation derived by riley and davis is equivalent to that of a codimension one normal form xamination of the bifurcation structure of the normal form then leads to a description of the development of three dimensional interface patterns during unidirectional solidification the general methodology underlying this study is also discussed and conditions under which the method can be applied to other evolution equations are derived and clearly stated

global exponential stability and periodic solutions of cohen grossberg neural networks with continuously distributed delays abstract convergence dynamics of cohen grossberg neural networks cgnns with continuously distributed delays are discussed without assuming the differentiability and monotonicity of activation functions the differentiability of amplification functions and the symmetry of synaptic interconnection weights by skilfully constructing suitable lyapunov functionals and employing inequality technique three sets of easily verifiable delay independent criteria to guarantee the global exponential stability of a unique equilibrium point are given and moreover by constructing poincare mapping other three sets of easily verifiable delay independent criteria to assure the existence and globally exponential stability of periodic solutions are obtained six examples are given to illustrate the theoretical results

stability analysis of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract in this paper the problem of stability analysis for a class of impulsive stochastic cohen grossberg neural networks with mixed delays is considered the mixed time delays comprise both the time varying and infinite distributed delays by employing a combination of the m matrix theory and stochastic analysis technique a sufficient condition is obtained to ensure the existence uniqueness and exponential p stability of the equilibrium point for the addressed impulsive stochastic cohen grossberg neural network with mixed delays the proposed method which does not make use of the lyapunov functional is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and or distributed delays we then extend our main results to the case where the parameters contain interval uncertainties moreover the exponential convergence rate index is estimated which depends on the system parameters an example is given to show the effectiveness of the obtained results

speed of pulled fronts with a cutoff we study the effect of a small cutoff epsilon on the velocity of a pulled front in one dimension by means of a variational principle we obtain a lower bound on the speed dependent on the cutoff for which the two leading order terms correspond to the brunet derrida expression to do so we cast a known variational principle for the speed of propagation of fronts in different variables which makes it more suitable for applications

speed of wave front solutions to hyperbolic reaction diffusion equations the asymptotic speed problem of front solutions to hyperbolic reaction diffusion hrd equations is studied in detail we perform linear and variational analyses to obtain bounds for the speed in contrast to what has been done in previous work here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds for some functions it is possible to determine the speed without any uncertainty this is also achieved for some systems of hrd i e time delayed lotka volterra equations that take into account the interaction among different species an analytical analysis is performed for several systems of biological interest and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently s1063 651x 99 06211 x

exponential stability and oscillation of hopfield graded response neural network both exponential and stochastic stabilities of the hopfield neural network are analyzed the results are especially useful for analyzing the stabilities of asymmetric neural networks a constraint on the connection matrix has been found under which the neural network has a unique and exponentially stable equilibrium given any connection matrix this constraint can be satisfied through the adjustment of the gains of the amplifiers and the resistances in the neural net circuit a one to one and smooth map between input currents and the equilibria of the neural network can be set up the above results can be applied to the master slave net to prove that the master net can find the best connection matrix for the slave net for the neural network disturbed by some noise the stochastic stability of the network is also analyzed a special asymmetric neural network formed by a closed chain of formal neurons is also studied for its stability and oscillation both stable and oscillatory dynamics are obtained in the closed chain network through the adjustment of the gains and resistances of the amplifiers

on the principal bifurcation branch of a third order nonlinear long wave equation we study the principal bifurcation curve of a third order equation which describes the nonlinear evolution of several systems with a long wavelength instability we show that the main bifurcation branch can be derived from a variational principle this allows us to obtain a close estimate of the complete branch in particular when the bifurcation is subcritical the large amplitude stable branch can be found in a simple manner

order and complexity in the kuramoto sivashinsky model of weakly turbulent interfaces abstract we present a large number of new geometric ergodic and statistical properties of the kuramoto sivashinsky equation modeling interfacial turbulence in various physical contexts in addition this equation has the remarkable property of inertial manifolds where some finite dimensional dynamical system is rigorously equivalent to this infinite dimensional partial differential equation in moderate size domains up to ten periods in length a low dimensional vector field skeleton underpins even strongly chaotic regimes and controls the bifurcations of the inertial manifold the extreme numerical sensitivity of chaos in this dissipative pde requires very high precision methods despite the geometrical complexities of the bifurcation structure some statistical properties remain remarkably simple there is overwhelming evidence that for some parameter values a permanent unsteady state exists an unexpectedly simple diffusive relaxation of the large scale fluctuations is extracted from extensive numerical simulations in these calculations we observe long time tails for the correlation functions of relevant quantities we propose an explanation in terms of an effective viscosity and compare the transport in the weakly turbulent interface with related theories for random interfaces and developed turbulence

an exactly solvable travelling wave equation in the fisher kpp class for a simple one dimensional lattice version of a travelling wave equation we obtain an exact relation between the initial condition and the position of the front at any later time this exact relation takes the form of an inverse problem given the times t n at which the travelling wave reaches the positions n one can deduce the initial profile we show by means of complex analysis that a number of known properties of travelling wave equations in the fisher kpp class can be recovered in particular bramson s shifts of the positions we also recover and generalize ebert van saarloos corrections depending on the initial condition

long wave morphological instabilities in the directional solidification of a dilute binary mixture long wave instabilities in a directionally solidified binary mixture may occur in several limits sivashinsky identified a small segregation coefficient limit and obtained a weakly nonlinear evolution equation governing subcritical two dimensional bifurcation brattkus and davis identified a near absolute stability limit and obtained a strongly nonlinear evolution equation governing supercritical two dimensional bifurcation the present investigation identifies a third strongly nonlinear evolution equation arising in the small segregation coefficient large surface energy limit this equation links both of the former and describes the change from the sub to super critical bifurcations this study sets the previous long wave analyses into a logical framework

planar solitary and spiral waves of the burgers cgl equations for flames governed by a sequential reaction this paper studied the planar solitary and spiral waves of the coupled burgers complex ginzburg landau burgers cgl equations which were derived from the nonlinear evolution of the coupled long scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chemical reaction having two flame fronts corresponding to two reaction zones with a finite separation distance between them first some exact solutions including the planar and solitary waves for the one dimensional burgers cgl equations that are obtained by subtle transforms and the hyperbolic tangent function expansion method second some spiral waves for the two dimensional burgers cgl equations are investigated the existence of the spiral waves is proved rigorously by schauder s fixed point theorem applied to a class of functions and the approximate solutions are also obtained by the power series expansion method furthermore some numerical simulations are carried out near 0 r 1 since the

laminarizing effects of dispersion in an active dissipative nonlinear medium abstract the kuramoto sivashinsky equation has become a popular prototype for systems which exhibit spatial temporal chaos we show here that a linear dispersion term h xxx tends to arrest such irregular behavior in favor of spatially periodic cellular structures as is consistent with prior numerical and experimental observations the study includes a normal form analysis and a numerical investigation of periodic and solitary stationary wave solutions of the equation it is shown that by 1 1 the infinite families of stationary periodic waves of the kuramoto sivashinsky equation each ending in a solitary wave have been annihilated successively such that only a lone family of periodic waves consisting of one hump kdv pulses for 3 7 remains as the only periodic stationary wave attractors of the system these periodic waves have much larger domains of attraction than the strange attractors and hence tend to dominate spatial temporal chaos in an extended domain with significant dispersion

minimal speed of fronts of reaction convection diffusion equations we study the minimal speed of propagating fronts of convection reaction diffusion equations of the form u t microphi u u x u xx f u for positive reaction terms with f 0 0 the function phi u is continuous and vanishes at u 0 a variational principle for the minimal speed of the waves is constructed from which upper and lower bounds are obtained this permits the a priori assessment of the effect of the convective term on the minimal speed of the traveling fronts if the convective term is not strong enough it produces no effect on the minimal speed of the fronts we show that if f u sqrt f 0 microphi u 0 then the minimal speed is given by the linear value 2sqrt f 0 and the convective term has no effect on the minimal speed the results are illustrated by applying them to the exactly solvable case u t microuu x u xx u 1 u results are also given for the density dependent diffusion case u t microphi u u x d u u x x f u

variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation we give an integral variational characterization for the speed of fronts of the nonlinear diffusion equationut uxx f u withf 0 f 1 0 andf 0 in 0 1 which permits in principle the calculation of the exact speed for arbitraryf