We give a rigorous mathematical analysis of the one-soliton solution of the focusing Davey-Stewartson II equation and a proof of its instability under perturbation. Building on the fundamental perturbation analysis of Gadyl'shin and Kiselev, we verify their Assumption 1 and use Fredholm determinants to globalize their perturbation analysis.
|Number of pages||36|
|State||Published - Aug 2 2018|
Bibliographical noteFunding Information:
It is a pleasure to thank Ken McLaughlin, Peter Miller, Michael Music, Katharine Ott, and Brad Schwer for helpful discussions. We are grateful to the referees for a very careful reading of the manuscript and a number of suggestions which improved the paper. This work was supported in part by grants from the National Science Foundation (DMS-1208778, PAP) and from the Simons Foundation/SFARI (359431, PAP and 422756, RMB).
1 Brown supported in part by Simons Collaboration Grant 422756. 2 Perry supported in part by NSF grant DMS-1208778 and Simons Collaboration Grant 359431. 3 Appendix B written by Russell M Brown and Peter Perry. 4 Author to whom any correspondence should be addressed.
© 2018 IOP Publishing Ltd & London Mathematical Society.
- Davey-Stewartson equation
- inverse scattering
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy (all)
- Applied Mathematics