Two-dimensional integrable generalization of the Camassa-Holm equation

DOI10.1016/S0375-9601(99)00536-8zbMath0935.37032OpenAlexW2053587698MaRDI QIDQ1966960

A. I. Zenchuk, Roberto A. Kraenkel

Publication date: 8 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(99)00536-8

zbMATH Keywords

Camassa-Holm equationshallow-water theory\((2+1)\) solitary-wave like solutions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves for incompressible inviscid fluids (76B25) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (15)

Stability of negative solitary waves for a generalized Camassa-Holm equation with quartic nonlinearity ⋮ Differential form method for finding symmetries of a \((2+1)\)-dimensional Camassa-Holm system based on its Lax pair ⋮ Integrable generalization of the modified Camassa-Holm equation in \(2 + 1\) dimensions ⋮ Non-Isospectral 1+1 Hierarchies Arising from a Camassa Holm Hierarchy in 2+1 Dimensions ⋮ Obtaining multisoliton solutions of the \((2+1)\)-dimensional Camassa-Holm system using Darboux transformations ⋮ Multidimensional hierarchies of (1+1)-dimensional integrable partial differential equations. Nonsymmetric ∂̄-dressing ⋮ Dirichlet series and the integrability of multilinear differential equations ⋮ Peakon, compacton and loop excitations with periodic behavior in KdV type models related to Schrödinger system ⋮ Local discontinuous Galerkin methods for the two-dimensional Camassa-Holm equation ⋮ Modified Korteweg-de Vries hierarchy with hodograph transformation: Camassa-Holm and Harry-Dym hierarchies ⋮ The spectral problem and particular solutions to the \((2+1)\)-dimensional integrable generalization of the Camassa-Holm equation ⋮ A note on the Painlevé analysis of a \((2+1)\)-dimensional Camassa-Holm equation ⋮ Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa-Holm equation ⋮ The stability of exact solitary wave solutions for simplified modified Camassa-Holm equation ⋮ Error estimates of the local discontinuous Galerkin methods for two-dimensional \((\mu)\)-Camassa-Holm equations

Cites Work

• Unnamed Item
• On a class of physically important integrable equations
• An integrable shallow water equation with peaked solitons
• Camassa-Holm equation: transformation to deformed sinh-Gordon equations, cuspon and soliton solutions
• Model equations for long waves in nonlinear dispersive systems

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