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 |
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| [8] | DOI: 10.1088/0951-7715/3/2/010 · Zbl 0727.35111 · doi:10.1088/0951-7715/3/2/010 |
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