Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 4290-4325 |
| Number of pages | 36 |
| Journal | Nonlinearity |
| Volume | 31 |
| Issue number | 9 |
| DOIs | |
| State | Published - Aug 2 2018 |
Bibliographical note
Publisher Copyright:© 2018 IOP Publishing Ltd & London Mathematical Society.
Funding
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.
| Funders | Funder number |
|---|---|
| PAP | |
| Simons Collaboration | 422756 |
| Simons Foundation/SFARI | |
| National Science Foundation (NSF) | DMS-1208778, 359431 |
Keywords
- Davey-Stewartson equation
- Solitons
- inverse scattering
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics