Cipolatti, Rolci On the existence of standing waves for a Davey-Stewartson system. (English) Zbl 0762.35109 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. Cited in 1 ReviewCited in 38 Documents 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 PDF BibTeX XML Cite \textit{R. Cipolatti}, Commun. Partial Differ. Equations 17, No. 5--6, 967--988 (1992; Zbl 0762.35109) Full Text: DOI OpenURL 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· Zbl 0727.35111 [9] Ghidaglia J.M., Weinstein M.I. Standing waves for a Davey-Stewartson System, unpublished.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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.