In this paper, we consider the transverse instability for a nonlinear Schrödinger equation with a linear potential on R×TL, where 2πL is the period of the torus TL. 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×TL. We show the stability of line standing waves for all L > 0 by using the argument of the previous paper .
|Number of pages||34|
|Journal||Advances in Differential Equations|
|Publication status||Published - 2016|
All Science Journal Classification (ASJC) codes
- Applied Mathematics