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

By Ming Chen, Si‐Qi Liu, You-jin Zhang. 2005

353 citations recorded by the source corpus.

An explicit reciprocal transformation between a two-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

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b5c176e3fa0fc436387548746075e4292c8f3443

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In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Well-posedness and blow-up solution for a modified two-component periodic Camassa–Holm system with peakons (2010, neutral): “[7,18,25] and references therein.”
Wave Breaking and Global Existence for a Generalized Two-Component Camassa–Holm System (2010, background): “[1, 9, 26, 43, 45].”
On a Camassa-Holm type equation with two dependent variables (2005, background): “Still more recently, related equations have been considered in [ 8 ], within the framework of reciprocal transformations, and the properties of solitary waves and two-particle like solutions described.”
On the Cauchy problem for the two-component Camassa–Holm system (2011, background): “[1,6,20,25].”
A three-component generalization of Camassa–Holm equation with N-peakon solutions (2011, background): “Recently, a two-component generalization of the CH equation has been proposed [9,20] and it has bi-Hamiltonian structure and multi-kink solutions [9,20,2].”