Integrable Models for Shallow Water with Energy Dependent Spectral Problems
- 10.1142/S1402925112400086How to use a DOI?
- Inverse scattering method; nonlinear evolution equations; solitons
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.
- © 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
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 -