Darboux transformation and multi-soliton solutions of the Camassa-Holm equation and modified Camassa-Holm equation
Darboux transformation and multi-soliton solutions of the Camassa-Holm equation and modified Camassa-Holm equation
复制标题
DOI：
10.1063/1.4964256
复制
发表时间：
2015-06
期刊：
影响因子：
--
通讯作者：
B. Xia;Ruguang Zhou;Z. Qiao
中科院分区：
文献类型：
--
作者：
B. Xia;Ruguang Zhou;Z. Qiao
In this paper, we propose a new approach to calculate multi-soliton solutions of Camassa-Holm (CH) equation and modified Camassa-Holm (MCH) equation with aid of Darboux transformation (DT). The new approach simplifies the approach presented in {\it Proc. R. Soc. Lond. A} {\bf 460} 2617-2627 (2004). We first map the CH and MCH equation to a negative order KdV (NKdV) equation by a reciprocal transformation. Then we proceed to apply the DT to solve the NKdV equation in the usual way. Finally we invert the reciprocal transformation to recover the solutions of the CH equation and MCH equation.
