Stability of Solitary Waves for a Generalized Derivative Nonlinear Schrödinger Equation

Abstract

We consider a derivative nonlinear Schrödinger equation with a general nonlinearity. This equation has a two parameter family of solitary wave solutions. We prove orbital stability/instability results that depend on the strength of the nonlinearity and, in some instances, their velocity. We illustrate these results with numerical simulations.

29 pages, 4 Figures