Solitons of shallow-water models from energy-dependent spectral problems
Department of Science, Waterford Institute of Technology, Cork Road, Waterford, Ireland
2 Department of Computing and Mathematics, Waterford Institute of Technology, Cork Road, Waterford, Ireland
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Accepted: 31 December 2017
Published online: 18 January 2018
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 of energy-dependent spectral problems for the system, which we then use to construct the solution of this hydrodynamic system.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018