Related papers: Orbital stability property for coupled nonlinear S…
It is shown that plane wave solutions to the cubic nonlinear Schr\"odinger equation on a torus behave orbitally stable under generic perturbations of the initial data that are small in a high-order Sobolev norm, over long times that extend…
We consider the one-dimensional nonlinear Schr\"odinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family of solitary wave solutions in both the focusing and…
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…
A nonlinear Schr\"odinger equation for the envelope of two dimensional surface water waves on finite depth with non zero constant vorticity is derived, and the influence of this constant vorticity on the well known stability properties of…
In this paper, we are concerned with solutions to the following nonlinear Schr\"odinger equation with combined inhomogeneous nonlinearities, $$ -\Delta u + \lambda u= \mu |x|^{-b}|u|^{q-2} u + |x|^{-b}|u|^{p-2} u \quad \mbox{in} \,\, \R^N,…
Plane wave solutions to the cubic nonlinear Schr\"odinger equation on a torus have recently been shown to behave orbitally stable. Under generic perturbations of the initial data that are small in a high-order Sobolev norm, plane waves are…
The present paper deals with sufficient conditions for orbital stability of periodic waves of a general class of evolution equations supporting nonlinear dispersive waves. Our method can be seen as an extension to spatially periodic waves…
In this article, we focus on the stability of dark solitons for a general one-dimensional nonlinear Schr\"odinger equation. More precisely, we prove the orbital stability of a chain of travelling waves whose speeds are well ordered, taken…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
This paper studies the nonlinear stability of capillary-gravity waves propagating along the interface dividing two immiscible fluid layers of finite depth. The motion in both regions is governed by the incompressible and irrotational Euler…
We consider a nonlinear Schr\"{o}dinger (NLS) equation with any positive power nonlinearity on a star graph $\Gamma$ ($N$ half-lines glued at the common vertex) with a $\delta$ interaction at the vertex. The strength of the interaction is…
Some focusing coupled Schrodinger equations are investigated. First, existence of ground state is obtained. Second, global and non global existence of solutions are discussed via potential-well method. Finally, strong instability of…
The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of…
The classical Schr\"odinger equation with a harmonic trap potential $V(x)=|x|^2$, describing the quantum harmonic oscillator, has been studied quite extensively in the last twenty years. Its ground states are bell-shaped and unique, among…
The stability and dynamical properties of the so-called resonant nonlinear Schr\"odinger (RNLS) equation, are considered. The RNLS is a variant of the nonlinear Schr\"odinger (NLS) equation with the addition of a perturbation used to…
In this paper we consider the nonlinear fractional logarithmic Schr\"{o}dinger equation. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. We also prove…
This paper is devoted to the study of the nonlinear Schr\"odinger-Poisson system with a doping profile. We are interested in the existence of stable standing waves by considering the associated $L^2$-minimization problem. The presence of a…
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…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
The parametrically driven, damped nonlinear Schr\"odinger equation has two cn- and two dn-wave solutions. We show that one pair of the cn and dn solutions is unstable for any combination of the driver's strength, dissipation coefficient and…