Journal of Nonlinear Mathematical Physics

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Volume 19, Issue Supplement 1, November 2012, Pages 72 - 88

Integrable Models for Shallow Water with Energy Dependent Spectral Problems

Authors
Rossen Ivanov*, Tony Lyons†
School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland
Received 13 March 2012, Accepted 20 April 2012, Available Online 28 November 2012.
DOI
10.1142/S1402925112400086How to use a DOI?
Keywords
Inverse scattering method; nonlinear evolution equations; solitons
Abstract

We study the inverse problem for the so-called operators with energy depending potentials. In particular, we study spectral operators with quadratic dependence on the spectral parameter. The corresponding hierarchy of integrable equations includes the Kaup–Boussinesq equation. We formulate the inverse problem as a Riemann–Hilbert problem with a ℤ2 reduction group. The soliton solutions are explicitly obtained.

Copyright
© 2012 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
19 - Supplement 1
Pages
72 - 88
Publication Date
2012/11/28
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925112400086How to use a DOI?
Copyright
© 2012 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Rossen Ivanov
AU  - Tony Lyons
PY  - 2012
DA  - 2012/11/28
TI  - Integrable Models for Shallow Water with Energy Dependent Spectral Problems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 72
EP  - 88
VL  - 19
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112400086
DO  - 10.1142/S1402925112400086
ID  - Ivanov2012
ER  -