Eur. Phys. J. Plus (2022) 137: 96
https://doi.org/10.1140/epjp/s13360-022-02342-1

Regular Article

Lie symmetry transformation, conservation laws and nonlinear self-adjointness of (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Prayagraj, India

^b kumarimanju@mnnit.ac.in

Received: 1 September 2021
Accepted: 30 December 2021
Published online: 8 January 2022

Abstract

In the present letter, we have derived some group invariant solutions of (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation (DJKM). Using the Lie symmetry approach, the nonlinear DJKM equation can be reduced to an ordinary differential equation (ODE). Making the number of independent variables lesser in each leading stage can form a reduced ODE. Further, for some parametric restrictions on the formed ODE, solutions are constructed. All the results are extensively rich in physical context due to the presence of arbitrary constants and functions occurring initially in the infinitesimal generators. The condition for nonlinear self-adjointness has been made for the DJKM equation. Eventually, we established conservation laws of the equation with their respective Lie symmetry. Thereafter, we performed a numerical simulation to trace and study the dynamical behavior of the solutions via their graph using MATLAB codes.