New Exact Solutions of Date Jimbo Kashiwara Miwa Equation Using Lie Symmetry Groups

Abstract

In this article, new exact solutions of $\left(2+1\right)$ -dimensional Date Jimbo Kashiwara Miwa (DJKM) equation are constructed by applying the Lie symmetry method. By considering similarity variables obtained through Lie symmetry generators, considered $\left(2+1\right)$ -dimensional DJKM equation is transformed into a linear partial differential equation with reduction of one independent variable. Afterwards by using Lie symmetry generators of this linear PDE, different invariant solutions involving exponential and logarithmic functions are explored which lead to the new exact solutions of the DJKM equation. Graphical representations of the obtained solutions are also presented to show the significance of the current work.