Resonant soliton interaction for the Date–Jimbo–Kashiwara–Miwa equation

Abstract

Investigated in this paper is the resonant soliton interactions for the ($2+1$)-dimensional Date–Jimbo–Kashiwara–Miwa equation. A comprehensive classification of these interactions is presented, based on the exact expression of resonant soliton branches derived from asymptotic analysis. Two types of resonant interactions between two solitons are identified, characterized by the parameter $A_{ij}$, which directly determines the phase shift. One-resonant and two-resonant three-soliton interactions are discussed, in which certain new soliton branches are revealed. Some graphical analyses are provided to illustrate these resonant interactions.