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

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 determinants. The large time asymptotic of the solution is derived with the formula 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 is also considered, showing that it reproduces the known result.