Stability of Solitary Waves for a Generalized Derivative Nonlinear Schrödinger Equation

2012/06/15 by Liu, Xiao, Simpson, Gideon, Sulem, Catherine
#35A15 #35B35 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)

paper · doi:10.48550/arxiv.1206.3502

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.

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