Solitons of shallow-water models from energy-dependent spectral problems
arXiv:1705.04989
Abstract
The current work investigates the soliton solutions of the Kaup-Boussinesq equation using the Inverse Scattering Transform method. We outline the construction of the Riemann-Hilbert problem for a pair energy-dependent spectral problems for the system, which we then use to construct the solution of this hydrodynamic system.