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

Cipolatti, Rolci

Commun. Partial Differ. Equations 17, No. 5-6, 967-988 (1992).

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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