Differential and Integral Equations

Stability and instability of standing waves for the generalized Davey-Stewartson system

Masahito Ohta

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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.

Article information

Source
Differential Integral Equations, Volume 8, Number 7 (1995), 1775-1788.

Dates
First available in Project Euclid: 12 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1368397756

Mathematical Reviews number (MathSciNet)
MR1347979

Zentralblatt MATH identifier
0827.35122

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

Citation

Ohta, Masahito. Stability and instability of standing waves for the generalized Davey-Stewartson system. Differential Integral Equations 8 (1995), no. 7, 1775--1788. https://projecteuclid.org/euclid.die/1368397756


Export citation