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arXiv · 1506.08639

Darboux transformation and multi-soliton solutions of the Camassa-Holm equation and modified Camassa-Holm equation

Baoqiang Xia·Ruguang Zhou·Zhijun Qiao
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Abstract

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.

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Baoqiang Xia, Ruguang Zhou, Zhijun Qiao. 2015-09-11. Darboux transformation and multi-soliton solutions of the Camassa-Holm equation and modified Camassa-Holm equation. https://doi.org/10.1063/1.4964256

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