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Home / Applicable Analysis, Volume 88, Number 1

Instability of standing waves for a weakly coupled non-linear Schrodinger system

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Authors: Shu, Ji 1 ; Zhang, Jian 2 ; 

Source: Applicable Analysis, Volume 88, Number 1, January 2009, pp. 53-62(10)

Publisher: Taylor and Francis Ltd

DOI: https://doi.org/10.1080/00036810802555466

This article discusses the weakly coupled non-linear Schrodinger equations. With the variational characterization of the ground state solutions, the potential well argument and the concavity method, we derive a sharp condition for blow-up and global existence to the solutions of the Cauchy problem. At the same time, we also prove the instability of standing waves.

Keywords: blow-up; global existence; ground state; standing wave; weakly coupled non-linear Schrodinger equations

Document Type: Research Article

Affiliations: 1: Sichuan Provincial Key Laboratory of Computer Software, Sichuan Normal University, Chengdu, P.R. China,College of Mathematics and Software Science, Sichuan Normal University, Chengdu, P.R. China 2: College of Mathematics and Software Science, Sichuan Normal University, Chengdu, P.R. China

Publication date: 01 January 2009

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