Integrable Models for Shallow Water with Energy Dependent Spectral Problems

DOI10.1142/S1402925112400086zbMath1362.37111arXiv1211.5567OpenAlexW3098606353MaRDI QIDQ5737707

Tony Lyons, Rossen I. Ivanov

Publication date: 30 May 2017

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.5567

zbMATH Keywords

solitonsnonlinear evolution equationsinverse scattering method

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (11)

The dynamics of flat surface internal geophysical waves with currents ⋮ Energy-dependent reflectionless inverse scattering ⋮ Linear stability of exact solutions for the generalized Kaup-Boussinesq equation and their dynamical evolutions ⋮ Hamiltonian model for coupled surface and internal waves in the presence of currents ⋮ Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom ⋮ Traveling wave solutions of degenerate coupled Korteweg-de Vries equation ⋮ Formation of the undular bores in shallow water generalized Kaup-Boussinesq model ⋮ Invariant solutions and conservation laws of the generalized Kaup–Boussinesq equation ⋮ Liouville correspondences between multicomponent integrable hierarchies ⋮ Integration of the Kaup-Boussinesq system with time-dependent coefficients ⋮ The generalized KaupߝBoussinesq equation: multiple soliton solutions

Cites Work

• Integrable Hamiltonian hierarchies. Spectral and geometric methods
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