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2010•Communications in Theoretical PhysicsOpen access

On Camassa–Holm Equation with Self-Consistent Sources and Its Solutions

Huang Ye-Hui, Yao Yu-Qin, Zeng Yun-Bo

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Abstract

Regarded as the integrable generalization of Camassa–Holm (CH) equation, the CH equation with self-consistent sources (CHESCS) is derived. The Lax representation of the CHESCS is presented. The conservation laws for CHESCS are constructed. The peakon solution, N-soliton, N-cuspon, N-positon, and N-negaton solutions of CHESCS are obtained by using Darboux transformation and the method of variation of constants.

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Regarded as the integrable generalization of Camassa–Holm (CH) equation, the CH equation with self-consistent sources (CHESCS) is derived. The Lax representation of the CHESCS is presented. The conservation laws for CHESCS are constructed. The peakon solution, N-soliton, N-cuspon, N-positon, and N-negaton solutions of CHESCS are obtained by using Darboux transformation and the method of variation of constants.

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Available abstract

Regarded as the integrable generalization of Camassa–Holm (CH) equation, the CH equation with self-consistent sources (CHESCS) is derived. The Lax representation of the CHESCS is presented. The conservation laws for CHESCS are constructed. The peakon solution, N-soliton, N-cuspon, N-positon, and N-negaton solutions of CHESCS are obtained by using Darboux transformation and the method of variation of constants.

Key concepts: Camassa–Holm equation, Self consistent, Physics, Mathematical physics, Quantum electrodynamics, Integrable system

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