Smooth and peaked solitons of the CH equation

DOI10.1088/1751-8113/43/43/434003zbMath1202.35226arXiv1003.1338OpenAlexW2058412910MaRDI QIDQ3057416

Darryl D. Holm, Rossen I. Ivanov

Publication date: 24 November 2010

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.1338

zbMATH Keywords

Riemann-Hilbert problempeaked solitonCamassa-Holm shallow water wave equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) 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) Asymptotic expansions of solutions to PDEs (35C20) Soliton equations (35Q51) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08)

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Liouville correspondences between integrable hierarchies ⋮ New variational and multisymplectic formulations of the Euler–Poincaré equation on the Virasoro–Bott group using the inverse map ⋮ Geometric numerical integrators for Hunter-Saxton-like equations ⋮ Bell polynomial approach to associated Camassa-Holm equation ⋮ Norm Inflation and Ill-Posedness for the Degasperis-Procesi Equation ⋮ Peakon solutions of Alice-Bob \(b\)-family equation and Novikov equation ⋮ Multisoliton solutions of the two-component Camassa–Holm system and their reductions ⋮ Non-uniqueness for the ab-family of equations ⋮ Multiple soliton solutions for a new generalization of the associated Camassa-Holm equation by exp-function method ⋮ Multicomponent Fokas–Lenells equations on Hermitian symmetric spaces ⋮ Bäcklund transformation and smooth multisoliton solutions for a modified Camassa-Holm equation with cubic nonlinearity ⋮ Integrable generalization of the associated Camassa-Holm equation ⋮ A multi-symplectic numerical integrator for the two-component Camassa–Holm equation ⋮ A view of the peakon world through the lens of approximation theory

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