Parametric Representation for the Multisoliton Solution of the Camassa-Holm Equation

Details Parametric Representation for the Multisoliton Solution of the Camassa-Holm Equation Parametric Representation for the Multisoliton Solution of the Camassa-Holm Equation

2005-04-26

arxiv.org/abs/nlin/0504055v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages

Scientific paper

10.1143/JPSJ.74.1983

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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