We use the ∂-inverse scattering method to obtain global well-posedness and large-time asymptotics for the defocussing Davey-Stewartson II equation. We show that these global solutions are dispersive by computing their leading asymptotic behavior as t → ∞ in terms of an associated linear problem. These results appear to be sharp.
|Number of pages||53|
|Journal||Journal of Spectral Theory|
|State||Published - 2016|
Bibliographical noteFunding Information:
Supported in part by NSF Grants DMS-0710477 and DMS-1208778. Supported in part by NSF grant DMS-0901569. It is a pleasure to thank Russell Brown, Ken McLaughlin, Michael Music, and Peter Topalov for helpful discussions, to thank Russell Brown, Peter Miller, and Katharine Ott for a careful reading of the manuscript, and to thank Michael Christ and Catherine Sulem for helpful correspondence. I am also grateful to the referee for an exceptionally thorough and meticulous reading of three (!) versions of this manuscript, for pointing out several errors in an earlier version of this paper, and for numerous helpful suggestions which have considerably improved the manuscript. The current proof of Lemma 3.11 incorporates a suggestion of the referee. Part of this work was carried out at the Mathematical Sciences Research Institute in Berkeley, California, whose hospitality the author gratefully acknowledges.
© European Mathematical Society.
- Davey-Stewartson equation
- Inverse scattering
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Geometry and Topology