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May/June 2016 Transverse instability for nonlinear Schrödinger equation with a linear potential
Yohei Yamazaki
Adv. Differential Equations 21(5/6): 429-462 (May/June 2016).

Abstract

In this paper, we consider the transverse instability for a nonlinear Schrödinger equation with a linear potential on ${\mathbb {R} \times \mathbb {T}_L}$, where $2\pi L$ is the period of the torus $\mathbb{T}_L$. Rose and Weinstein [18] 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 ${\mathbb R}$ as a line standing wave of nonlinear Schrödinger equation on ${\mathbb R} \times {\mathbb T}_L$. We show the stability of line standing waves for all $L>0$ by using the argument of the previous paper [26].

Citation

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Yohei Yamazaki. "Transverse instability for nonlinear Schrödinger equation with a linear potential." Adv. Differential Equations 21 (5/6) 429 - 462, May/June 2016.

Information

Published: May/June 2016
First available in Project Euclid: 9 March 2016

zbMATH: 1344.35142
MathSciNet: MR3473581

Subjects:
Primary: 35B32 , 35B35 , 35Q55

Rights: Copyright © 2016 Khayyam Publishing, Inc.

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Vol.21 • No. 5/6 • May/June 2016
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