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.

Keywords:

• Rational solutions
• time-dependent DJKM equation
• interaction phenomena
• lump solutions

2010 Mathematics Subject Classification:

• Computational solitions

Disclosure statement

No potential conflict of interest was reported by the author(s).