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 12 reduction group. The soliton solutions are explicitly obtained.
Original language | English |
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Article number | 1240008 |
Journal | Journal of Nonlinear Mathematical Physics |
Volume | 19 |
Issue number | SUPPL. 1 |
DOIs | |
Publication status | Published - Oct 2012 |
Keywords
- Inverse scattering method
- nonlinear evolution equations
- solitons