Soliton dynamics to the multi-component complex coupled integrable dispersionless equation

• We propose multi-component complex model equations starting from the complex coupled integrable dispersionless equation.
• We show the integrability of the complex coupled systems by exhibiting the Lax pairs.
• We present multi-soliton solutions by Hirota’s bilinear method and N-soliton solutions in Pfaffians form.
• Dynamics of one- and two-soliton solutions are investigated in details.

The generalized coupled integrable dispersionless (CID) equation describes the current-fed string in a certain external magnetic field. In this paper, we propose a multi-component complex CID equation. The integrability of the multi-component complex equation is confirmed by constructing Lax pairs. One-soliton and two-soliton solutions are investigated to exhibit rich evolution properties. Especially, similar as the multi-component short pulse equation and the first negative AKNS equation, periodic interaction, parallel solitons, elastic and inelastic interaction, energy re-distribution happen between two solitons. Multi-soliton solutions are given in terms of Pfaffian expression by virtue of Hirota’s bilinear method.