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On the instability of ground states for a Davey-Stewartson system. (English) Zbl 0784.35106

The author considers the equation \(iu_ t+\Delta u+bE_ 1\bigl( | u |^ 2 \bigr) u-a | u |^ \alpha u=0\) in \(\mathbb{R}^ n\), for \(n=2,3\), and he shows that if \(\varphi\) is a ground state and \(a(\alpha- 2) \leq 0\), the set \(\Omega_ \varphi=\bigl\{ e^{i\theta} (\cdot+y);\;\theta \in \mathbb{R},\;y \in \mathbb{R}^ n \bigr\}\) is unstable by the flow of the equation.
Reviewer: I.Vrabie (Iaşi)

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B35 Stability in context of PDEs
37C10 Dynamics induced by flows and semiflows
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References:

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