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.


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
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