## 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

### Keywords:

standing wave; ground states; unstable set
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### References:

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