Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Applied mathematics
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.
DOI
https://doi.org10.1142/S1402925112400086
Recommended Citation
R. Ivanov and T. Lyons, Integrable models for shallow water with energy dependent spectral problems, Journal of Nonlinear Mathematical Physics, Vol. 19, Suppl. 1 (2012) 1240008 (17 pages) DOI: 10.1142/S1402925112400086
Funder
Science Foundation Ireland
Included in
Mathematics Commons, Non-linear Dynamics Commons, Partial Differential Equations Commons
Publication Details
Journal of Nonlinear Mathematical Physics,
Vol. 19, Suppl. 1 (2012) 1240008 (17 pages)
DOI: 10.1142/S1402925112400086