Transverse instability for nonlinear Schrödinger equation with a linear potential

2015/05/03 by Yamazaki, Yohei · 1 citation
#35B32 #35B35 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.00421

Abstract

In this paper we consider the transverse instability for a nonlinear Schrödinger equation with a linear potential on ℝ × \mathbbT_L, where 2πL is the period of the torus \mathbbT_L. Rose and Weinstein showed the existence of a stable standing wave for a nonlinear Schrödinger equation with a linear potential. We regard the standing wave of nonlinear Schrödinger equation on ℝ as a line standing wave of nonlinear Schrödinger equation on ℝ × \mathbbT_L. We show the stability of line standing waves for all L>0.

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• Numerical study of transverse (in-)stability of solitary waves in the cubic-quintic nonlinear Schrödinger equation

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