Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation

Abstract

In this article, we construct loop soliton solutions and mixed soliton - loop soliton solution for the Degasperis-Procesi equation. To explore these solutions we adopt the procedure given by Matsuno. By appropriately modifying the $\tau$-function given in the above paper we derive these solutions. We present the explicit form of one and two loop soliton solutions and mixed soliton - loop soliton solutions and investigate the interaction between (i) two loop soliton solutions in different parametric regimes and (ii) a loop soliton with a conventional soliton in detail.

Published in Physica Scripta (2012)

References in corpus (4)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Inverse Scattering Transform for the Degasperis-Procesi Equation
• Degasperis-Procesi peakons and the discrete cubic string
• A New Integrable Equation with Peakon Solutions