Vector multi-pole solutions in the [formula omitted]-coupled Hirota equation

Abstract

In this paper, we study the vector multi-pole (MP) solutions of the r-coupled Hirota equation (RCHE). First of all, based on the Darboux transformation and the N-soliton solution, we derive the explicit formulas of the arbitrary-order vector MP solutions. Then, through the balance between exponential and algebraic terms, we give all asymptotic solitons in the vector double- and triple-pole solutions via an asymptotic analysis method. Furthermore, we analyze the soliton interactions in vector MP solutions. By comparing with the scalar Hirota equation, we find that the RCHE has richer collision properties: the position shift of each component soliton grows logarithmically with r, the asymptotic solitons have the same shape in each component, and their amplitudes are proportional among the components.