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

Russell M. Brown; Peter A. Perry

doi:10.1088/1361-6544/aacc46

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

Russell M. Brown, Peter A. Perry

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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	https://doi.org/10.1088/1361-6544/aacc46
State	Published - 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.

Keywords

Davey-Stewartson equation
Solitons
inverse scattering

ASJC Scopus subject areas

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

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10.1088/1361-6544/aacc46

Cite this

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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.",

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N2 - 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.

AB - 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.

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KW - inverse scattering

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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