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arXiv · 1508.00247

Multi-soliton solution to the two-component Hunter-Saxton equation

Bao-Feng Feng·Senyue Lou·Ruoxia Yao
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Abstract

In this paper, we study the bilinear form and the general N-soliton solution for a two-component Hunter-Saxton (2-HS) equation, which is the short wave limit of a twocomponent Camassa-Holm equation. By defining a hodograph transformation based on a conservation law and appropriate dependent variable transformations, we propose a set of bilinear equations which yields the 2-HS equation. Furthermore, we construct the N-soliton solution to the 2-HS equation based on the tau functions of an extended two-dimensional Toda-lattice hierarchy through reductions. One- and two-soliton solutions are calculated and analyzed.

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Bao-Feng Feng, Senyue Lou, Ruoxia Yao. 2015-08-02. Multi-soliton solution to the two-component Hunter-Saxton equation. https://arxiv.org/abs/1508.00247

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