相关论文: Multiple permanent-wave trains in nonlinear system…
Linear stability of multi-vector-soliton bound states in the coupled nonlinear Schr\"odinger equations is analyzed using a new tail-matching method. Under the condition that individual vector solitons in the bound states are…
We study *infinite soliton trains* solutions of nonlinear Schr\"odinger equations (NLS), i.e. solutions behaving at large time as the sum of infinitely many solitary waves. Assuming the composing solitons have sufficiently large relative…
In this note we construct mixed dimensional infinite soliton trains, which are solutions of nonlinear Schr\"odinger equations whose asymptotic profiles at time infinity consist of infinitely many solitons of multiple dimensions. For example…
We prove the existence of a new type of solutions to a nonlinear Schr\"odinger system. These solutions, which we call "multi-speeds solitary waves", are behaving at large time as a couple of scalar solitary waves traveling at different…
We look for solutions to generic nonlinear Schr\"odinger equations build upon solitons and kinks. Solitons are localized solitary waves and kinks are their non localized counter-parts. We prove the existence of infinite soliton trains, i.e.…
We will first review known results on multi-solitons of dispersive partial differential equations, which are special solutions behaving like the sum of many weakly-interacting solitary waves. We will then describe our recent joint work with…
We consider coupled nonlinear Schrodinger equations (CNLSE) which govern the propagation of nonlinear waves in bimodal optical fibers. The nonlinear transform of a dual-frequency signal is used to generate an ultra-short-pulse train. To…
We investigate the dissipative dynamics of linear and nonlinear waves in harmonic traps by means of engineered complex non-Hermitian potentials. By combining an analytical mapping between real and complex Schr\"odinger equations with direct…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
This work is divided into two parts. First, we analyze the existence of positive bound and ground states for a second order stationary system coming from a coupled system of nonlinear Schr\"odinger--Korteweg-de Vries equations. Second, we…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\"odinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to…
Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a…
Coupling of chaotic oscillators has evidenced conditions where synchronization is possible, therefore a nonlinear system can be driven to a particular state through input from a similar oscillator. Here we expand this concept of control of…
We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed,…
A fully nonlinear, time-asymptotic theory of resonant particle trapping in large-amplitude quasi-parallel Alfven waves is presented. The effect of trapped particles on the nonlinear dynamics of quasi-stationary Alfvenic discontinuities and…
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…
This article provides a naturel sequel of previous works [6, 4] regarding the stability of travelling waves for a general one-dimensional Schr\"odinger equation (N LS) with non-zero condition at infinity. The aim of this article is twofold.…
The long-time asymptotics is analyzed for finite energy solutions of the 1D discrete Schr\"odinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group. For initial states…