Translator Disclaimer
1995 Stability and instability of standing waves for the generalized Davey-Stewartson system
Masahito Ohta
Differential Integral Equations 8(7): 1775-1788 (1995).

Abstract

We study the stability and instability properties of standing waves for the equation $iu_t+\Delta u+a\vert u\vert^{p-1}u+E_1(\vert u\vert^2)u=0$ in $\Bbb R^2$ or $\Bbb R^3$, which derives from the generalized Davey-Stewartson system in the elliptic-elliptic case. We show that if $n=2$ and $a(p-3)<0$, then the standing waves generated by the set of minimizers for the associated variational problem are stable. We also show that if $n=3$, $a>0$ and $1+4/3<p<5$ or $a<0$ and $1<p<3$, then the standing waves are strongly unstable. We employ the concentration compactness principle due to Lions and the compactness lemma due to Lieb to solve the associated minimization problem.

Citation

Download Citation

Masahito Ohta. "Stability and instability of standing waves for the generalized Davey-Stewartson system." Differential Integral Equations 8 (7) 1775 - 1788, 1995.

Information

Published: 1995
First available in Project Euclid: 12 May 2013

zbMATH: 0827.35122
MathSciNet: MR1347979

Subjects:
Primary: 35Q55
Secondary: 35B35

Rights: Copyright © 1995 Khayyam Publishing, Inc.

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.8 • No. 7 • 1995
Back to Top