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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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References:

[1] Berestycki H., Arch. Rach Mech. Anal 82 pp 313– (1983)
[2] Bergh J., Interpolation Spaces (1976)
[3] Cazenave T., Research Notes in Math. 89 (1983)
[4] Cazenave T., An introduction to nonlinear Schrödinger equations 22 (1989)
[5] DOI: 10.1098/rspa.1974.0076 · Zbl 0282.76008
[6] Folland G. B., Lectures on partial differential equations (1983) · Zbl 0529.35005
[7] Ghidaglia J. –M., I 308, in: C.R. Acad. Sci. Paris pp 115– (1989)
[8] DOI: 10.1088/0951-7715/3/2/010 · Zbl 0727.35111
[9] Ghidaglia J.M., Weinstein M.I. Standing waves for a Davey-Stewartson System, unpublished.
[10] Lions P. –L., Ann. Inst. H. Poincaré Analyse non linéaire 1 pp 109– (1984)
[11] Lions P. –L., Ann. Inst. H. Poincaré Analyse non linéaire 1 pp 223– (1984)
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