Multi-soliton solution to the two-component Hunter-Saxton equation
Exactly Solvable and Integrable Systems
2015-08-04 v1
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.
Keywords
Cite
@article{arxiv.1508.00247,
title = {Multi-soliton solution to the two-component Hunter-Saxton equation},
author = {Bao-Feng Feng and Senyue Lou and Ruoxia Yao},
journal= {arXiv preprint arXiv:1508.00247},
year = {2015}
}
Comments
17 pages, 4 figures