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On the instability of ground states for a Davey-Stewartson system. (English) Zbl 0784.35106
The author considers the equation $iu\sb t+\Delta u+bE\sb 1\bigl( \vert u \vert\sp 2 \bigr) u-a \vert u \vert\sp \alpha u=0$ in $\bbfR\sp n$, for $n=2,3$, and he shows that if $\varphi$ is a ground state and $a(\alpha- 2) \le 0$, the set $\Omega\sb \varphi=\bigl\{ e\sp{i\theta} (\cdot+y);\ \theta \in \bbfR,\ y \in \bbfR\sp n \bigr\}$ is unstable by the flow of the equation.
Reviewer: I.Vrabie (Iaşi)

MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
35B35Stability of solutions of PDE
37C10Vector fields, flows, ordinary differential equations
WorldCat.org
Full Text: Numdam EuDML
References:
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