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

TL;DR

This paper constructs explicit multi-loop soliton solutions for the Degasperis-Procesi equation using a modified tau-function approach, analyzing their interactions and dynamics.

Contribution

It introduces a method to derive explicit multi-loop and mixed soliton solutions for the Degasperis-Procesi equation, expanding understanding of their interactions.

Findings

Explicit one and two loop soliton solutions are derived.

Interactions between different types of solitons are analyzed.

Solutions reveal complex soliton interaction behaviors.

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.