A Study on Resonant Multisoliton Solution for the (2+1)‐Dimensional Date–Jimbo–Kashiwara–Miwa Equation With Variable Coefficients

ABSTRACT The resonant multisoliton for the ‐dimensional Date–Jimbo–Kashiwara–Miwa equation with variable coefficients is studied using the Hirota bilinear method. The bilinear form is given for the first time. When or , the resonance collision between two solitons occurs, resulting in Y‐shaped soliton. It turns out that this is not a completely elastic collision. Otherwise, when the condition or is satisfied, the collision between two solitons occurs, resulting in X‐shaped soliton. It is found that this is a completely elastic collision. The X‐shaped and Y‐shaped solitons are studied deeply, and the resonant collision process of the two solitons is explored. Some sufficient conditions based on parameters are given. Astonishingly, it is found that and affect the phase displacement trajectory of two solitons after resonance collision.