Construction of abundant solutions of the (2+1)-dimensional time-dependent Date–Jimbo–Kashiwara–Miwa equation

Abstract

Investigated in the current paper is the time-dependent Date–Jimbo–Kashiwara–Miwa equation in (2+1)-dimensions which works as a model for describing the propagation of nonlinear dispersive waves in inhomogeneous media. By implementing the homoclinic test method, the breather-kink wave solution to the considered equation is first generated. Then, based on the resulting solution and a parameter transformation, the double-solitary wave solution is obtained. Finally, the rogue wave emerges by taking a limit behavior. Meanwhile, some graphs are made to shed light on the structural characteristics.