Parametric Representation for the Multisoliton Solution of the Camassa-Holm Equation
Exactly Solvable and Integrable Systems
2009-11-11 v1
Abstract
The parametric representation is given to the multisoliton solution of the Camassa-Holm equation. It has a simple structure expressed in terms of determinants. The proof of the solution is carried out by an elementary theory of determinanats. The large time asymptotic of the solution is derived with the fomula for the phase shift. The latter reveals a new feature when compared with the one for the typical soliton solutions. The peakon limit of the phase shift ia also considered, showing that it reproduces the known result.
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Cite
@article{arxiv.nlin/0504055,
title = {Parametric Representation for the Multisoliton Solution of the Camassa-Holm Equation},
author = {Yoshimasa Matsuno},
journal= {arXiv preprint arXiv:nlin/0504055},
year = {2009}
}
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14 pages