Rational solutions, and the interaction solutions to the (2+1)-dimensional time-dependent Date-Jimbo-Kashiwara-Miwa equation

Abstract

In this work, the Date-Jimbo-Kashiwara-Miwa (DJKM) equation include time-dependent in (2 + 1)-dimensions that characterize the propagation of nonlinear dispersive waves in inhomogeneous media is studied. We construct rational solutions and the interaction physical phenomena between rational solution and multi-soliton wave to the time-dependent DJKM equation. The multi-soliton solutions are revealed by using the Hirota simple method, and then via the long-wave method, the M-lump solutions for two types of time-dependent are derived. Moreover, the interaction phenomena between rational solution and single-, double-soliton solutions are studied.