A Two-component Generalization of the Camassa-Holm Equation and its Solutions

2005/01/20 by Ming Chen, Si-Qi Liu, Si‐Qi Liu +1 · 363 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Camassa–Holm equation #Chemistry #Component (thermodynamics) #Flow (mathematics) #Generalization #Geometry #Hierarchy #Integrable system #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Peakon #Philosophy #Physics #Pure mathematics #Reciprocal #Thermodynamics #Transformation (genetics) #nlin.SI

paper · pdf · doi:10.1007/s11005-005-0041-7

published in Letters in Mathematical Physics 75(1), 1-15 (Springer Science+Business Media) · 15 pages, 16 figures, some typos corrected

arxiv created 2005/01/20 · openalex publication_date 2006/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

An explicit reciprocal transformation between a 2-component generalization of the Camassa-Holm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy is established, this transformation enables one to obtain solutions of the 2-CH system from those of the first negative flow of the AKNS hierarchy. Interesting examples of peakon and multi-kink solutions of the 2-CH system are presented.

Citations

• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• The Camassa-Holm Equation: A Loop Group Approach
• The Complex Geometry of Weak Piecewise Smooth Solutions of Integrable Nonlinear PDE's¶of Shallow Water and Dym Type

Cited by

• Vector peakon equations and isospectral flows in Clifford algebras
• Geometric Flows of Curves, Two-Component Camassa-Holm Equation and Generalized Heisenberg Ferromagnet Equation
• Vlasov moment flows and geodesics on the Jacobi group
• A Lagrangian View on Complete Integrability of the Two-Component Camassa–Holm System
• A two-component μ-Hunter–Saxton equation
• A Note on Traveling Wave Solutions to the Two Component Camassa–Holm Equation
• On negative flows of the AKNS hierarchy and a class of deformations of a bihamiltonian structure of hydrodynamic type
• On the Cauchy problem for a new integrable two-component system with peakon and weak kink solutions
• A new two-component integrable system with peakon solutions
• Singular solutions of a modified two-component Camassa-Holm equation
• The 2-component dispersionless Burgers equation arising in the modelling of blood flow