## On the existence of standing waves for a Davey-Stewartson system.(English)Zbl 0762.35109

Summary: We consider the standing waves for the Davey-Stewartson system $iu_ t+\Delta u=a| u|^ \alpha u+b_ 1uv_{x_ 1},\quad -\Delta v=b_ 2(| u|^ 2)_{x_ 1}$ in $$\mathbb{R}^ 2$$ and $$\mathbb{R}^ 3$$. By reducing this system to a single nonlinear equation of Schrödinger type, we study the existence, the regularity and asymptotics of ground states.

### MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35Q35 PDEs in connection with fluid mechanics 35B65 Smoothness and regularity of solutions to PDEs 35B10 Periodic solutions to PDEs

### Keywords:

variation method; regularity; asymptotics of ground states
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### References:

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