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

In this paper, we construct loop soliton solutions and mixed soliton-loop soliton solutions for the Degasperis-Procesi equation. To explore these solutions, we adopt the procedure given by Matsuno (2005 Inverse Problems 21 1553). 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.