direct approach to the study of soliton perturbations a direct approach in studying the soliton perturbations of nonlinear evolution equations has been developed it is based on the method of the derivative expansions for linearization of the perturbed equations and the separation of variables for solution of the linearized equations if differs substantially from the past direct methods the apparent advantage of this approach is that it relies on no knowledge of the inverse scattering transform besides it is very concise and easy to understand as an example we use it to study the perturbed korteweg de vries equation the results we obtained agree with what other authors have found

discretization behaviors of equivalent control based sliding mode control systems in this note discretization behaviors of the equivalent control based sliding mode control smc systems are studied some inherent dynamical properties of the discretized second order systems are first explored upper bounds for the system steady states are established the system s steady state behaviors are discussed the analysis for the second order systems is then extended to higher order systems simulations are presented to verify the theoretical results

evolution of a modulated kp soliton the author investigates the propagation of an initial profile consisting of a planar kp soliton with some small modulations using the solution of the cauchy problem for the linearized kp equation find that for large times the modulations move away from the peak of the profile leaving behind a stable soliton a generalization of this method is formulated for the study of the stability of solutions of other integrable equations

initial value problem of the linearized benjamin ono equation and its applications we consider the initial value problem of the benjamin ono bo equation linearized about the n soliton solution by establishing the completeness relation for the eigenfunctions of the linearized bo equation we construct the explicit solution to this problem as an application of the above result we investigate the linear stability of the n soliton solution we show that the wave under consideration is stable against infinitesimal perturbations thus we have a direct multisoliton perturbation theory for the bo equation without recourse to the inverse scattering transform in particular we can handle the first order solution beyond the adiabatic approximation the completeness relation established here enables us to give a general scheme for evaluating the first order correction to the leading order n soliton solution we also demonstrate that the first order solution satisfies an infinite set of conservation laws modified by the perturbations finally in the one soliton case we perform explicit calcu

adaptive sliding mode control in discrete time systems abstract discrete time sliding mode control is considered the case of known parameters is first analyzed leading to a new definition of the so called equivalent control as the piecewise constant control that reduces to zero in finite time the distance of the system state from the sliding manifold in the presence of bounded parametric uncertainties an adaptive control scheme that guarantees the asymptotic satisfaction of the same control objective is presented the main feature of this approach is the reduction of the order of the relevant error equation and the possibility of dealing with the nonmatched uncertainties introduced by the sampling process

evolution of solitary waves for a perturbed nonlinear schrodinger equation soliton perturbation theory is used to determine the evolution of a solitary wave described by a perturbed nonlinear schrodinger equation perturbation terms which model wide classes of physically relevant perturbations are considered an analytical solution is found for the first order correction of the evolving solitary wave this solution for the solitary wave tail is in integral form and an explicit expression is found for large time singularity theory usually used for combustion problems is applied to the large time expression for the solitary wave tail analytical results are obtained such as the parameter regions in which qualitatively different types of solitary wave tails occur the location of zeros and the location and amplitude of peaks in the solitary wave tail two examples the near continuum limit of a discrete nls equation and an explicit numerical scheme for the nls equation are considered in detail for the discrete nls equation it is found that three qualitatively different types of solitary wave tail can occur while for the explicit finite difference scheme only one type of solitary wave tail occurs an excellent comparison between the perturbation solution and numerical simulations for the solitary wave tail is found for both examples

first order soliton perturbation theory for a generalized kdv model with stochastic forcing and damping we discuss an application of the expansion method to the soliton perturbation theory for a generalized kdv model with stochastic forcing and damping we find that the expansion method is a perturbation technique which allows one to retain a more representative linearization for a nonlinear differential equation than comparable methods of perturbation such as those relying on small parameters indeed one primary benefit of the method is that it tends to provide much more reasonable solutions with relatively few terms compared to standard perturbation methods due to the more accurate linearization we show that the method allows one to obtain first order perturbations in which the stochastic and nonlinear contributions separate allowing one to study each influence independently at least to first order we then apply the expansion method to the study of a stochastic generalized kdv model and we show that this procedure gives a natural extension to the perturbation theory for the traditional kdv model the actual method of computation is outlined and may be applied to a variety of generalized kdv models

exploring the connection between quasistationary and squared eigenfunction expansion techniques in soliton perturbation theory abstract we give a short review of the techniques that have been used to study soliton perturbations for nonlinear integrable systems in 1 1 dimensions in particular we discuss the connection between direct perturbation methods using squared eigenfunction expansions and quasistationary perturbation theory we show for the kdv korteweg de vries how the results for quasistationary approximations are related to those for the standard adiabatic perturbation theory

monte carlo sampling in fractal landscapes we design a random walk to explore fractal landscapes such as those describing chaotic transients in dynamical systems we show that the random walk moves efficiently only when its step length depends on the height of the landscape via the largest lyapunov exponent of the chaotic system we propose a generalization of the wang landau algorithm which constructs not only the density of states transient time distribution but also the correct step length as a result we obtain a flat histogram monte carlo method which samples fractal landscapes in polynomial time a dramatic improvement over the exponential scaling of traditional uniform sampling methods our results are not limited by the dimensionality of the landscape and are confirmed numerically in chaotic systems with up to 30 dimensions

projected single spin flip dynamics in the ising model we study transition matrices for projected dynamics in the energy magnetization magnetization and energy spaces several single spin flip dynamics are considered such as the glauber and metropolis canonical ensemble dynamics and the metropolis dynamics for three multicanonical ensembles the flat energy magnetization the flat energy and the flat magnetization histograms from the numerical diagonalization of the matrices for the projected dynamics we obtain the subdominant eigenvalues and the largest relaxation times for systems of varying size although the projected dynamics is an approximation to the full state space dynamics comparison with some available results obtained by other authors shows that projection in the magnetization space is a reasonably accurate method to study the scaling of relaxation times with system size for each system size the transition matrices for arbitrary single spin flip dynamics are obtained from a single monte carlo estimate of the infinite temperature transition matrix this makes the method an efficient tool for evaluating the relative performance of any arbitrary local spin flip dynamics we also present results for appropriately defined average tunneling times of magnetization and compare their finite size scaling exponents with results of energy tunneling exponents available for the flat energy histogram multicanonical ensemble

the perturbed korteweg de vries equation considered anew the perturbed korteweg de vries equation is studied in a new way by a green s function formalism without use of inverse scattering methods the green s function is determined by employing the backlund transformation and green s theorem after a thorough analysis of the exact first order solution with regard to secular terms a two time scale expansion leads to the adiabatic approximation and the first order correction in accordance with the results of karpman and maslov contrary to statements in the literature the term tanh2 z in the expression for the modified phase of the perturbed soliton arises as a consequence of the systematically conducted first order perturbation theory

applying discrete time proportional integral observers for state and disturbance estimations in this note we apply the proportional integral observer to simultaneously estimate system states and unknown disturbances for discrete time nonminimum phase systems conditions for providing the existence of such observer are given when the disturbances do not vary too much between two consecutive sampling instances the proposed method can render the estimation errors of system states and disturbances to be constrained in a small bounded region simulation results support the theoretical developments

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

renormalization group theory for perturbed evolution equations we show that proto rg renormaliation group theory can be used to give a systematic description of the evolution of soltion of perturbed equations the equations describing the deformation of its shape as the effect of perturbation are proto rg equations the rg approach may be simpler than inverse scattering theory ist and another approaches because it dose not rely on any knowledge of ist it is very concise and easy to understand

conservation laws and the perturbed kdv equation examines the integral for the correction to the soliton position in the adiabatic approximation using the modified conservation laws for the mass and the energy the general correction to the soliton position is obtained it is easily seen that this correction is due to the formation of the shelf

a method to compute statistics of large noise induced perturbations of nonlinear schrodinger solitons we describe in detail the application of importance sampling to numerical simulations of large noise induced perturbations in soliton based optical transmission systems governed by the nonlinear schrodinger equation the method allows one to concentrate the samples in monte carlo simulations around those noise realizations that are most likely to produce the large pulse deformations connected with errors and it yields computational speedups of several orders of magnitude over standard monte carlo simulations we demonstrate the method by using it to calculate the probability density functions associated with pulse amplitude frequency timing and phase fluctuations in a prototypical soliton based communication system

reconstructing sliding surfaces for siso variable structure output feedback control systems using inverse method there exists a dynamic mapping relationship between the sliding variable and the output variable in a linear time invariant lti single input single output siso system this relationship is invariant of the matched disturbances which lies in the control space in this note a continuous time dynamic inverse compensator is proposed to reconstruct the sliding variable from the system output this inverse compensator is stable and causal provided that the original siso system is minimum phase and that the input output relative degree is less than or equal to one in case the system relative degree is greater than one a digital approximation for the inverse compensator is introduced to track the sliding variable in discrete time to the accuracy of o t where t is the sampling period thus the discrete time variable structure control vsc law can be implemented without full state accessibility

the analytical evolution of nls solitons due to the numerical discretization error soliton perturbation theory is used to obtain analytical solutions describing solitary wave tails or shelves due to numerical discretization error for soliton solutions of the nonlinear schrodinger equation two important implicit numerical schemes for the nonlinear schrodinger equation with second order temporal and spatial discretization errors are considered these are the crank nicolson scheme and a scheme due to taha 1 based on the inverse scattering transform the first order correction for the solitary wave tail or shelf is in integral form and an explicit expression is found for large time the shelf decays slowly at a rate of which is characteristic of the nonlinear schrodinger equation singularity theory usually used for combustion problems is applied to the explicit large time expression for the solitary wave tail analytical results are then obtained such as the parameter regions in which qualitatively different types of solitary wave tails occur the location of zeros and the location and amplitude of peaks it is found that three different types of tail occur for the crank nicolson and taha schemes and that the taha scheme exhibits some unusual symmetry properties as the tails for left and right moving solitary waves are different optimal choices of the discretization parameters for the numerical schemes are also found which minimize the amplitude of the solitary wave tail the analytical solutions are compared with numerical simulations and an excellent comparison is found

quasi stationary perturbations of the kdv soliton in this paper we show how the results of quasi stationary perturbation theory relate to those based upon squared eigenfunction expansions we show that the two give the same results for a quasi stationary approximation and also show how standard adiabatic perturbation theory connects to the quasi stationary theory

pruned enriched rosenbluth method simulations of θ polymers of chain length up to 1 000 000 we present an algorithm for simulating flexible chain polymers it combines the rosenbluth rosenbluth method with recursive enrichment although it can be applied also in more general situations it is most efficient for three dimensional theta polymers on the simple cubic lattice there it allows high statistics simulations of chains of length up to n 10 sup 6 for storage reasons this is feasable only for polymers in a finite volume for free theta polymers in infinite volume we present very high statistics runs with n 10000 these simulations fully agree with previous simulations made by hegger and grassberger j chem phys bold 102 6681 1995 with a similar but less efficient algorithm showing that logarithmic corrections to mean field behavior are much stronger than predicted by field theory but the finite volume simulations show that the density inside a collapsed globule scales with the distance from the theta point as predicted by mean field theory in contrast to claims in the work mentioned above in addition to the simple cubic lattice we also studied two versions of the bond fluctuation model but with much shorter chains finally we show that our method can be applied also to off lattice models and illustrate this with simulations of amore model studied in detail by freire ital et al macromolecules bold 19 452 1986 and later work copyright ital 1997 ital the american physical society less

internal modes of envelope solitons abstract we extend the concept of internal mode to envelope solitons and show that this mode is responsible for long lived weakly damped periodic oscillations of the soliton amplitude observed in numerical simulations we present analytical and numerical results for solitons of the generalized nonlinear schrodinger equation and analyze the example of the cubic quintic nonlinearity in more detail we obtain also analytical criteria for the existence and bifurcations of the soliton internal mode and calculate the rate of the radiation induced damping of the soliton oscillations induced by excitation of the internal mode

asymptotic stability of the toda m soliton we prove that multi soliton solutions of the toda lattice are both linearly and nonlinearly stable our proof uses neither the inverse spectral method nor the lax pair of the model but

the stochastic damped kdv equation the author applies singular perturbation theory to the study of a damped kdv soliton under the influence of space and time dependent external noise he finds that asymptotically the shape of the averaged solution approaches that of a gaussian packet whose amplitude decays and width grows in the same way as in the case of purely time dependent noise

complete eigenfunctions of linearized integrable equations expanded around a soliton solution complete eigenfunctions for an integrable equation linearized around a soliton solution are the key to the development of a direct soliton perturbation theory in this article we explicitly construct such eigenfunctions for a large class of integrable equations including the kdv nls and mkdv hierarchies we establish the striking result that the linearization operators of all equations in the same integrable hierarchy share the same complete set of eigenfunctions furthermore these eigenfunctions are precisely the squared eigenfunctions of the associated eigenvalue problem the key step in our derivation is to show that the linearization operator of an integrable equation can be factored into a function of the integro differential operator which generates the integrable equation and the linearization operator of the lowest order integrable equation in the same hierarchy we also obtain similar results for the adjoint linearization operator of an integrable equation even though our analysis is conducted only for the kdv nls and mkdv hierarchies similar results are expected for other integrable hierarchies as well we further explicitly present the complete eigenfunctions for the kdv nls and mkdv hierarchy equations and give their inner products thus they can be readily used to develop a direct soliton perturbation theory for any of those hierarchy equations

an o t sup 2 boundary layer in sliding mode for sampled data systems the use of a discontinuous control law typically sign functions in a sampled data system will bring about chattering phenomenon in the vicinity of the sliding manifold leading to a boundary layer with thickness o t where t is the sampling period however by proper consideration of the sampling phenomenon in the discrete time sliding mode control design the thickness of the boundary layer can be reduced to o t sup 2 in contrast to discontinuous control for continuous time vss the discrete time sliding mode control need not be of switching type

a direct perturbation theory for dark solitons based on a complete set of the squared jost solutions because of the essential difficulty caused by the non vanishing boundary condition a systematic perturbation approach for dark solitons has not yet been found based on a rigorous proof of the completeness of the squared jost solution with explicit expressions for one soliton case a direct perturbation approach for dark solitons is developed in this paper difficulties caused by the background are overcome as an example of the approach the problem of damping is treated as a perturbation

direct perturbation theory for a nearly integrable nonlinear equation with application to dark soliton solutions since the linearized equation for a nearly integrable nonlinear equation is essentially a linear equation the direct perturbation theory is now developed in the frame of green s function theory of linear differential equations the perturbed nls equation with normal dispersion is treated as an example some obscure points in previous works about this equation are clarified

a simple treatment of the sine gordon equation to avoid difficulties due to the complexity of the lax pair of the sine gordon equation the orthogonality relations of the squared jost solutions is derived simply using the 1 1 dimensional green s theorem the direct perturbation theory for sine gordon in the laboratory reference is re developed correcting some numerical coefficients in published orthogonality relationships

higher accuracy output feedback sliding mode control of sampled data systems the problem of output feedback sliding mode control for sampled data systems in the presence of external disturbances is considered the proposed output feedback control strategy helps obtain a quasi sliding mode with an o t 3 boundary layer where t is the sampling period this outperforms the o t 2 result induced by the one step delayed disturbance approximation method the proposed scheme is applicable to linear systems which are relative degree one and minimum phase an example is given to illustrate the efficacy of the new method

the density wave in a car following model according to the optimal velocity model the condition for stable traffic flow is deduced nonlinear analysis shows that the density fluctuation in traffic flow itself induces two types of local density waves a weak fluctuation occurring near the stability state in a wide range of headways forms a soliton determined by the korteweg de vries kdv equation the appearance of such a soliton shows that drivers tend to reach the safety distance when they are away from it this density wave degenerates to a travelling wave at the critical point a strong fluctuation occurring around the critical point forms a kink or a soliton determined by the modified korteweg de vries mkdv equation

on the discrete time integral sliding mode control a new discrete time integral sliding mode control dismc scheme is proposed for sampled data systems the new control scheme is characterized by a discrete time integral sliding manifold which inherits the desired properties of the continuous time integral sliding manifold such as full order sliding manifold with pole assignment and elimination of the reaching phase in particular comparing with existing discrete time sliding mode control the new scheme is able to achieve more precise tracking performance it will be shown in this work that the new control scheme achieves o t2 steady state error for state regulation with the widely adopted delay based disturbance estimation another desirable feature is the proposed dismc prevents the generation of overlarge control actions due to deadbeat response which is usually inevitable due to the existence of poles at the origin for a reduced order sliding manifold designed for sampled data systems both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme

a procedure for finding numerical trajectories on chaotic saddles abstract examples are common in dynamical systems in which there are regions containing chaotic sets that are not attractors if almost every trajectory eventually leaves some region but the region contains a chaotic set then typical trajectories will behave chaotically for a while and then will leave the region and so we will observe chaotic transients the main objective that will be addressed is the dynamic restraint problem given a region that contains a chaotic set but does not contain an attractor find a chaotic trajectory numerically that remains in the regionfor an arbituarily long period of time systems with horseshoes have such regions as do systems with fractal basin boundaries as does the henon map for suitably chosen parameters we present a numerical technique for finding trajectories which will stay in such chaotic sets for arbitrarily long periods of time and it leads to a saddle straddle trajectory the method is called the pim triple procedure since it is based on so called pim triples a pim proper interior maximum triple is three points a c b in a straight line segment such that the interior point c i e c is between a and b has the maximum escape time that is its escape time from the region is greater than the escape time of both a and b proper means the segment from a to b is smaller than a previously obtained segment we show rigorously that the pim triple procedure works in ideal situations we find it works well even in less than ideal cases this procedure can also be used for the computation of lyapunov exponents furthermore the accessible pim triple procedure a refined pim triple procedure for finding accessible trajectories on the chaotic saddle will also be discussed

lax pair operators for squared sum and squared difference eigenfunctions an interrelationship between various representations of the inverse scattering transformation is established by examining eigenfunctions of lax pair operators of the sine gordon equation and the modified korteweg de vries equation in particular it is shown explicitly that there exist lax pair operators for the squared sum and squared difference eigenfunctions of the ablowitz kaup newell segur inverse scattering transformation

reaching law for dsmc systems with relative degree 2 switching variable abstractthis paper presents the first attempt to design a reaching law based discrete time sliding mode controller with a relative degree 2 switching variable the current value of this variable is only affected by the control signal and disturbance generated two time instants ago it is demonstrated that the new reaching law based strategy offers a smaller quasi sliding mode band width when compared to a similar control scheme with relative degree 1 switching variable this in turn leads to reduced system output error in the control system proposed in the paper

fast algorithm to calculate density of states an algorithm to calculate the density of states based on the well known wang landau method is introduced independent random walks are performed in different restricted ranges of energy and the resultant density of states is modified by a function of time f t ensuremath propto t ensuremath 1 for large time as a consequence the calculated density of state g m e t approaches asymptotically the exact value g mathit ex e as ensuremath propto t ensuremath 1 2 avoiding the saturation of the error it is also shown that the growth of the interface of the energy histogram belongs to the random deposition universality class

systematic perturbation theory for sine gordon solitons without use of inverse scattering methods the perturbed sine gordon soliton solutions kinks breathers in laboratory coordinates are derived by a green function formalism in a novel way dispensing with any inverse scattering methods besides the backlund transformation a simple approach based on green s theorem is employed for determining the green functions a systematic treatment allows the adiabatic approximation to be derived in a new manner the results are compared to those of the relevant papers in this field and thereby further insight is provided in a simple example a kink scattered by an impurity the calculation of energy radiation is demonstrated

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

lax pairs spectral problems and recursion operators we present various examples for the connection between lax pairs and recursion operators from this connection a new method for constructing recursion operators is derived as an application we find recursion operators to some integrable equations newly found by wadati et al j phys soc jpn lett 46 1965 1979 j phys soc jpn 47 1698 1979

output feedback sliding mode control for sampled data systems we address the output feedback sliding mode control problem for a sampled data linear system with external disturbances of the matching type by taking into account the disturbance compensation a deadbeat high gain output feedback control strategy with additional dynamics is able to attenuate the disturbances in the framework of singular perturbation analysis it is shown that the closed loop system exhibits good robustness against exogenous disturbances

dynamical behaviors of an euler discretized sliding mode control systems the dynamical behaviors of an euler discretized sliding mode control smc systems based on equivalent control strategy are studied a periodic 2 orbit in steady state is found for the switching function of the euler discretized smc systems the time steps for the switching function to converge toward the periodic 2 orbit are obtained when the discretized smc system is stable it further shows that the system states of the smc systems will also enter into some periodic 2 orbits and these periodic 2 orbits are characterized by explicit analytic expressions finally simulation examples are given to illustrate the theoretical results

a direct approach to studying soliton perturbations starting with an integrable nonlinear evolution equation the author investigates perturbations about a one soliton solution through the inversion of a linear equation for the first order correction to the soliton solution this inversion differs from past methods as the proposed method takes place in coordinate space not spectral space while it employs some of the tools of inverse scattering theory the method is applied to the korteweg de vries nonlinear schrodinger and sine gordon equations the first order corrections are then obtained

thermal diffusion of boussinesq solitons we consider the problem of the soliton dynamics in the presence of an external noisy force for the boussinesq type equations a set of ordinary differential equations odes of the relevant coordinates of the system is derived we show that for the improved boussinesq ibq equation the set of odes has limiting cases leading to a set of odes which can be directly derived either from the ill posed boussinesq equation or from the korteweg de vries kdv equation the case of a soliton propagating in the presence of damping and thermal noise is considered for the ibq equation a good agreement between theory and simulations is observed showing the strong robustness of these excitations the results obtained here generalize previous results obtained in the frame of the kdv equation for lattice solitons in the monatomic chain of atoms

green s function method for perturbed dnls equation with the squared spectrum parameter abstract a general direct perturbation theory for the perturbed dnls equation is developed the completeness relation is given by the green s function method similar to that used for the linear equations the effect of damping on a single soliton is calculated as an example and the result is good with the squared spectrum parameter

squared eigenfunctions for the sasa satsuma equation squared eigenfunctions are quadratic combinations of jost functions and adjoint jost functions which satisfy the linearized equation of an integrable equation they are needed for various studies related to integrable equations such as the development of its soliton perturbation theory in this article squared eigenfunctions are derived for the sasa satsuma equation whose spectral operator is a 3 3 system while its linearized operator is a 2 2 system it is shown that these squared eigenfunctions are sums of two terms where each term is a product of a jost function and an adjoint jost function the procedure of this derivation consists of two steps first is to calculate the variations of the potentials via variations of the scattering data by the riemann hilbert method the second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations while this procedure has been used before on other integrable equations it is shown here for

δ modulated feedback in discretization of sliding mode control modulated feedback control introduces periodicity the global attracting property of the periodic points is established for a simple scalar discrete time system under d modulated feedback attracting regions of the periodic points are also characterized when the discretization effects of the equivalent control based sliding mode control systems are studied we show that the zero order hold discretization gives rise to d modulation in the sliding mode direction the global attracting property of d modulated feedback offers a vivid illustration of the way sliding is achieved interestingly we find that a zoh discretization scheme of the equivalent control based sliding mode control system with relative degree one results in only 2 periodic orbits

on the evolution of perturbations to solutions of the kadomtsev petviashvilli equation using the benney luke equation the benney luke equation which arises as a long wave asymptotic approximation of water waves contains the kadomtsev petviashvilli kp equation as a leading order maximal balanced approximation the question analyzed is how the benney luke equation modifies the so called web solutions of the kp equation it is found that the benney luke equation introduces dispersive radiation which breaks each of the symmetric soliton like humps well away from the interaction region of the kp web solution into a tail of multi peaked oscillating profiles behind the main solitary hump computation indicates that the wave structure is modified near the center of the interaction region both analytical and numerical techniques are employed for working with non periodic non decaying solutions on unbounded domains

a bayesian analysis of monte carlo correlation times for the two dimensional ising model abstract we present a new bayesian analysis of the high accuracy data of nightingale and blote for the correlation times of the two dimensional ising model to determine the value of the dynamical critical exponent we demonstrate the crucial role played by the nightingale blote assumption that odd terms disappear in their expression for the correlation time as a function of the size of the system we obtain differing results for the existence of logarithmic corrections and the value of the dynamical critical exponent depending on whether or not that assumption is valid

a perturbation method for dark solitons based on a complete set of the squared jost solutions a perturbation method for dark solitons is developed which is based on the construction and the rigorous proof of the complete set of squared jost solutions the general procedure solving the adiabatic solution of perturbed nonlinear schrodinger equation the time evolution equation of dark soliton parameters and a formula for calculating the first order correction are given the method can also overcome the difficulties resulting from the non vanishing boundary condition

optimized multicanonical simulations a proposal based on classical fluctuation theory we propose a recursive procedure to estimate the microcanonical density of states in multicanonical monte carlo simulations which relies only on measurements of moments of the energy distribution avoiding entirely the need for energy histograms this method yields directly a piecewise analytical approximation to the microcanonical inverse temperature e and allows improved control over the statistics and efficiency of the simulations we demonstrate its utility in connection with recently proposed schemes for improving the efficiency of multicanonical sampling either with adjustment of the asymptotic energy distribution or with the replacement of single spin flip dynamics with collective updates

discrete time terminal sliding mode control systems based on euler s discretization in this technical note the dynamical behaviors of discrete time terminal sliding mode control systems based on euler s discretization is investigated based on a recursive analysis the boundedness for the steady states of the system is established theoretical analysis shows that the discrete time terminal sliding mode control method can offer a higher output tracking precision than the discrete time linear sliding mode control method simulations are given to verify the theoretical results

a method to compute statistics of large noise induced perturbations of nonlinear schrodinger solitons we demonstrate in detail the application of importance sampling to the numerical simulation of large noise induced perturbations in soliton based optical transmission systems governed by the nonlinear schrodinger equation the method allows one to concentrate numerical monte carlo simulations around the noise realizations that are most likely to produce the large pulse deformations connected with errors and yields computational speedups of several orders of magnitude over standard monte carlo simulations we demonstrate the method by using it to calculate the probability density functions associated with pulse amplitude frequency and timing fluctuations in a prototypical soliton based communication system

solitary wave solutions for a coupled pair of mkdv equations propagation of weakly nonlinear long waves is studied within the framework of a system of two coupled modified korteweg de vries equations we investigate analytically and numerically the various families of soliton states for the considered model by scaling the functions and variables we find that the resulting coupled pair of equations has only one combined parameter this parameter depends on the wave speed and the coupling coefficient explicit analytical expressions for both of the symmetric and antisymmetric states are determined numerical method is derived to solve the proposed system many numerical tests have been conducted to study the behavior of the solution and the existence of the asymmetric soliton states is displayed numerically

nonlinear stability of gardner breathers abstract we show that breather solutions of the gardner equation a natural generalization of the kdv and mkdv equations are h 2 r stable through a variational approach we characterize gardner breathers as minimizers of a new lyapunov functional and we study the associated spectral problem through i the analysis of the spectrum of explicit linear systems spectral stability and i i controlling degenerated directions by using low regularity conservation laws

stability of position control of traveling waves in reaction diffusion systems we consider the stability of position control of traveling waves in reaction diffusion systems as proposed in l ober and engel phys rev lett 112 148305 2014 instead of analyzing the controlled reaction diffusion system stability is studied on the reduced level of the equation of motion for the position over time of perturbed traveling waves we find an interval of perturbations of initial conditions for which position control is stable this interval can be interpreted as a localized region where traveling waves are susceptible to perturbations for stationary solutions of reaction diffusion systems with reflection symmetry this region does not exist analytical results are in qualitative agreement with numerical simulations of the controlled schl ogl model

a perturbational approach to the two soliton systems abstract the two soliton systems of the perturbed non linear schrodinger nls and sine gordon sg equations are considered by means of a simple quasi particle approach in which the soliton interaction and the action of an external perturbation are described by the one soliton perturbation theory the method is quite general it does not assume the knowledge of the exact unperturbed multi soliton solutions it is restricted however by the requirement that the distances between the solitons must be large enough the validity of the approach is checked by applying it to some cases where it is possible to make a comparison with the inverse scattering method different types of soliton collisions and bound soliton systems are investigated in particular detailed descriptions of the two soliton systems of the double sg equations are presented

stability and evolution of solitary waves in perturbed generalized nonlinear schrodinger equations in this paper we study the stability and evolution of solitary waves in perturbed generalized nonlinear schrodinger nls equations our method is based on the completeness of the bounded eigenstates of the associated linear operator in l2 space and a standard multiple scale perturbation technique unlike the adiabatic perturbation method our method details all instability mechanisms caused by perturbations of such equations and explicitly specifies when such instabilities will occur in particular our method uncovers the instability caused by bifurcation of nonzero discrete eigenvalues of the linearization operator as an example we consider the perturbed cubic quintic nls equation in detail and determine the stability regions of its solitary waves in the instability region we also specify where the solitary waves decay collapse develop movingfronts or evolve into a stable spatially localized and temporally periodic state the generalization of this method to other perturbed nonlinear wave systems is also discussed