Advanced Studies in Pure Mathematics

Instability of standing waves for a system of nonlinear Schrödinger equations in a degenerate case

Shotaro Kawahara and Masahito Ohta

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Abstract

We study a system of nonlinear Schrödinger equations with cubic interactions in one space dimension. The orbital stability and instability of semitrivial standing wave solutions are studied for both non-degenerate and degenerate cases.

Article information

Source
Asymptotic Analysis for Nonlinear Dispersive and Wave Equations, K. Kato, T. Ogawa and T. Ozawa, eds. (Tokyo: Mathematical Society of Japan, 2019), 85-100

Dates
Received: 30 January 2016
Revised: 20 May 2016
First available in Project Euclid: 31 October 2019

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1572545241

Digital Object Identifier
doi:10.2969/aspm/08110085

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35B35: Stability

Keywords
nonlinear Schrödinger equations standing wave stability

Citation

Kawahara, Shotaro; Ohta, Masahito. Instability of standing waves for a system of nonlinear Schrödinger equations in a degenerate case. Asymptotic Analysis for Nonlinear Dispersive and Wave Equations, 85--100, Mathematical Society of Japan, Tokyo, Japan, 2019. doi:10.2969/aspm/08110085. https://projecteuclid.org/euclid.aspm/1572545241


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