Asymptotic Analysis and Soliton Interactions of the Multi-Pole Solutions in the Hirota Equation

Based on the Darboux transformation and N-soliton solutions, we obtain the explicit formulas of arbitrary-order multi-pole (MP) solutions of the Hirota equation via some limit technique. Then, by an improved asymptotic analysis method relying on the balance between exponential and algebraic terms, we derive the accurate expressions of all asymptotic solitons in the double- and triple-pole solutions. Moreover, we study the soliton interactions in the MP solutions and especially emphasize some unusual properties, like the interacting solitons separate from each other in a logarithmical law, the strengths of interaction forces decrease exponentially with their relative distances, and the constant-velocity asymptotic soliton does not experience a phase shift upon an interaction.