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The stability and dynamical properties of the so-called resonant nonlinear Schrodinger (RNLS) equation, are considered. The RNLS is a variant of the nonlinear Schrodinger (NLS) equation with the addition of a perturbation used to describe wave propagation in cold collisionless plasmas. We first examine the modulational stability of plane waves in the RNLS model, identifying the modifications of the associated conditions from the NLS case. We then move to the study of solitary waves with vanishing and nonzero boundary conditions. Interestingly the RNLS, much like the usual NLS, exhibits both dark and bright soliton solutions depending on the relative signs of dispersion and nonlinearity. The corresponding existence, stability and dynamics of these solutions are studied systematically in this work.
In this work, we study solitary waves in a (2+1)-dimensional variant of the defocusing nonlinear Schrodinger (NLS) equation, the so-called Camassa-Holm NLS (CH-NLS) equation. We use asymptotic multiscale expansion methods to reduce this model to a Ka
We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schrodinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the nonlocality-induced f
In this paper, we characterize a family of solitary waves for NLS with derivative (DNLS) by the structue analysis and the variational argument. Since (DNLS) doesnt enjoy the Galilean invariance any more, the structure analysis here is closely related
We study bifurcations and spectral stability of solitary waves in coupled nonlinear Schrodinger equations (CNLS) on the line. We assume that the coupled equations possess a solution of which one component is identically zero, and call it a $textit{fu
We discuss spatial dynamics and collapse scenarios of localized waves governed by the nonlinear Schr{o}dinger equation with nonlocal nonlinearity. Firstly, we prove that for arbitrary nonsingular attractive nonlocal nonlinear interaction in arbitrary