Darboux transformation and multi-soliton solutions of the Camassa-Holm equation and modified Camassa-Holm equation

DOI10.1063/1.4964256zbMath1351.37252arXiv1506.08639OpenAlexW3098691145MaRDI QIDQ2832730

Baoqiang Xia, Zhijun Qiao, Ruguang Zhou

Publication date: 14 November 2016

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

Full work available at URL: https://arxiv.org/abs/1506.08639

zbMATH Keywords

Camassa-Holm equationDarboux transformationmulti-soliton solutionsreciprocal transformation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) 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) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08)

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Nonlocal symmetries and Darboux transformations of the Camassa–Holm equation and modified Camassa–Holm equation revisited ⋮ Darboux transformation and novel solitons of a coupled system ⋮ On dynamics of multi-solitons for the good Boussinesq (gB) equation ⋮ Smooth multisoliton solutions of a 2-component peakon system with cubic nonlinearity ⋮ Continuous dependence and estimates of eigenvalues for periodic generalized Camassa-Holm equations ⋮ Solving the modified Camassa-Holm equation via the inverse scattering transform ⋮ An integrable semidiscretization of the modified Camassa–Holm equation with linear dispersion term ⋮ Multisoliton solutions of the two-component Camassa-Holm equation and its reductions ⋮ Multisoliton solutions of the Degasperis-Procesi equation and its shortwave limit: Darboux transformation approach ⋮ A new 3-component Degasperis-Procesi hierarchy ⋮ Integrable generalization of the modified Camassa-Holm equation in \(2 + 1\) dimensions ⋮ Decomposition of 2-Soliton Solutions for the Good Boussinesq Equations ⋮ Parametric multi-soliton solutions of a generalized Harry-Dym type equation ⋮ Soliton solutions to the Novikov equation and a negative flow of the Novikov hierarchy ⋮ Multi-soliton solutions of a two-component Camassa–Holm system: Darboux transformation approach ⋮ Obtaining multisoliton solutions of the \((2+1)\)-dimensional Camassa-Holm system using Darboux transformations ⋮ Solitons for the modified Camassa-Holm equation and their interactions via dressing method ⋮ Bäcklund transformations for the Camassa-Holm equation ⋮ A view of the peakon world through the lens of approximation theory ⋮ Darboux transformations of the Camassa-Holm type systems ⋮ The modified Camassa–Holm equation: Bäcklund transformation and nonlinear superposition formula

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