Related papers: Stability criterion for multi-component solitary w…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
We examine solitary waves in classical Heisenberg chains with an uniaxial anisotropy and a parallel magnetic field in a continuum approach. The boundary conditions commonly used are generalized to nonlinear spin wave states, which…
Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the…
We consider the nonlinear Klein-Gordon equation in $\R^d$. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the…
In this work, we revisit a criterion, originally proposed in [Nonlinearity {\bf 17}, 207 (2004)], for the stability of solitary traveling waves in Hamiltonian, infinite-dimensional lattice dynamical systems. We discuss the implications of…
In this work, we present a stability criteria for the solitary wave solutions to a BBM system that contains coupled nonlinear terms. Using the idea by Bona, Chen and Karakashian and exploiting the accurate point spectrum information of the…
We show global asymptotic stability of solitary waves of the nonlinear Schr\"odinger equation in space dimension 1. Furthermore, the radiation is shown to exhibit long range scattering if the nonlinearity is cubic at the origin, or standard…
We consider the nonlinear Dirac equation, also known as the Soler model: $i\p\sb t\psi=-i\alpha \cdot \nabla \psi+m \beta \psi-f(\psi\sp\ast \beta \psi) \beta \psi$, $\psi(x,t)\in\mathbb{C}^{N}$, $x\in\mathbb{R}^n$, $n\le 3$, $f\in C\sp…
We derive the precise stability criterion for smooth solitary waves in the b-family of Camassa-Holm equations. The smooth solitary waves exist on the constant background. In the integrable cases b = 2 and b = 3, we show analytically that…
We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…
We study the orbital stablity and instability of solitary wave solutions for nonlinear Schr\"odinger equations of derivative type.
Consider the one-dimensional $L^2$ supercritical nonlinear Schr\"odinger equation \begin{equation} i\partial_{t}\psi+\partial^{2}_{x}\psi+\vert \psi\vert^{2k}\psi=0 \text{, $k>2$}. \end{equation} It is well known that solitary waves for…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
Stability criteria have been derived and investigated in the last decades for many kinds of periodic traveling wave solutions to Hamiltonian PDEs. They turned out to depend in a crucial way on the negative signature of the Hessian matrix of…
We discuss the response of both moving and trapped solitary wave solutions of a nonlinear two-component nonlinear Schr\"odinger system in 1+1 dimensions to an anti-$\mathcal{PT}$ external periodic complex potential. The dynamical behavior…
In the present work, we consider the existence and spectral stability of multi-pulse solitary wave solutions to a nonlinear Schr\"odinger equation with both fourth and second order dispersion terms. We first give a criterion for the…
In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point…
We consider the focusing nonlinear Schr\"odinger equation on a large class of rotationally symmetric, noncompact manifolds. We prove the existence of a solitary wave by perturbing off the flat Euclidean case. Furthermore, we study the…
We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…
We determine the stability conditions for a radially symmetric noncommutative scalar soliton at finite noncommutivity parameter $\theta$. We find an intriguing relationship between the stability and existence conditions for all level-1…