On Camassa-Holm equation with self-consistent sources and its solutions
Yehui Huang, Yuqin Yao, Yunbo Zeng
TL;DR
This paper introduces the Camassa-Holm equation with self-consistent sources (CHESCS), derives its Lax pair, constructs conservation laws, and obtains various explicit solutions including peakons, solitons, cuspons, positons, and negaton solutions.
Contribution
It presents the first derivation of CHESCS, its Lax representation, conservation laws, and explicit solutions, extending the integrable Camassa-Holm framework.
Findings
Derived the Lax pair for CHESCS
Constructed conservation laws for CHESCS
Obtained explicit peakon, soliton, cuspon, positon, and negaton solutions
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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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Nonlinear Photonic Systems