Soliton solutions and their (in)stability for the focusing Davey-Stewartson II equation

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish
Pages (from-to)4290-4325
Number of pages36
Issue number9
StatePublished - Aug 2 2018

Bibliographical note

Funding 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).

Funding Information:
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.

Publisher Copyright:
© 2018 IOP Publishing Ltd & London Mathematical Society.


  • Davey-Stewartson equation
  • Solitons
  • inverse scattering

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy (all)
  • Applied Mathematics


Dive into the research topics of 'Soliton solutions and their (in)stability for the focusing Davey-Stewartson II equation'. Together they form a unique fingerprint.

Cite this