Transverse instability for nonlinear Schrödinger equation with a linear potential

Yohei Yamazaki

Transverse instability for nonlinear Schrödinger equation with a linear potential

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Abstract

In this paper, we consider the transverse instability for a nonlinear Schrödinger equation with a linear potential on R×T_L, where 2πL is the period of the torus 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 R as a line standing wave of nonlinear Schrödinger equation on R×T_L. We show the stability of line standing waves for all L > 0 by using the argument of the previous paper [26].

Original language	English
Pages (from-to)	429-462
Number of pages	34
Journal	Advances in Differential Equations
Volume	21
Issue number	5-6
Publication status	Published - 2016
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Cite this

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title = "Transverse instability for nonlinear Schr{\"o}dinger equation with a linear potential",

abstract = "In this paper, we consider the transverse instability for a nonlinear Schr{\"o}dinger equation with a linear potential on R×TL, where 2πL is the period of the torus TL. Rose and Weinstein [18] showed the existence of a stable standing wave for a nonlinear Schr{\"o}dinger equation with a linear potential. We regard the standing wave of nonlinear Schr{\"o}dinger equation on R as a line standing wave of nonlinear Schr{\"o}dinger equation on R×TL. We show the stability of line standing waves for all L > 0 by using the argument of the previous paper [26].",

author = "Yohei Yamazaki",

year = "2016",

language = "English",

volume = "21",

pages = "429--462",

journal = "Advances in Differential Equations",

issn = "1079-9389",

publisher = "Khayyam Publishing, Inc.",

number = "5-6",

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T1 - Transverse instability for nonlinear Schrödinger equation with a linear potential

AU - Yamazaki, Yohei

PY - 2016

Y1 - 2016

N2 - 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 [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 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 [26].

AB - 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 [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 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 [26].

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AN - SCOPUS:84971539274

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JO - Advances in Differential Equations

JF - Advances in Differential Equations

IS - 5-6

ER -

Transverse instability for nonlinear Schrödinger equation with a linear potential

Abstract

All Science Journal Classification (ASJC) codes

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