Transverse instability for a system of nonlinear schrödinger equations

Yohei Yamazaki

doi:10.3934/dcdsb.2014.19.565

Transverse instability for a system of nonlinear schrödinger equations

Yohei Yamazaki

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this paper, we consider the transverse instability for a system of nonlinear Schrödinger equations on R × T_L. Here, T _L means the torus with a 2πL period. It was shown by Colin-Ohta [11] that this system on R has a stable standing wave. In this paper, we regard this standing wave as the standing wave of this system on R × T _L. Then, we show that there exists the critical period Lσ which is the boundary between the stability and the instability of the standing wave on R × T_L.

Original language	English
Pages (from-to)	565-588
Number of pages	24
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	19
Issue number	2
DOIs	https://doi.org/10.3934/dcdsb.2014.19.565
Publication status	Published - Mar 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

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title = "Transverse instability for a system of nonlinear schr{\"o}dinger equations",

abstract = "In this paper, we consider the transverse instability for a system of nonlinear Schr{\"o}dinger equations on R × TL. Here, T L means the torus with a 2πL period. It was shown by Colin-Ohta [11] that this system on R has a stable standing wave. In this paper, we regard this standing wave as the standing wave of this system on R × T L. Then, we show that there exists the critical period Lσ which is the boundary between the stability and the instability of the standing wave on R × TL.",

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AB - In this paper, we consider the transverse instability for a system of nonlinear Schrödinger equations on R × TL. Here, T L means the torus with a 2πL period. It was shown by Colin-Ohta [11] that this system on R has a stable standing wave. In this paper, we regard this standing wave as the standing wave of this system on R × T L. Then, we show that there exists the critical period Lσ which is the boundary between the stability and the instability of the standing wave on R × TL.

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