Lie Symmetry Analysis and Some Exact Solutions of (2+1)-dimensional KdV-Burgers Equation

Abstract

In this work, the Lie group method is used to perform the similarity reduction and to obtain the exact solutions of the $$(2+1)$$ -dimensional KdV-Burgers equation. Similarity transformation method reduces $$(2+1)$$ -dimensional KdV-Burgers equation into $$(1+1)$$ -dimensional PDEs, later it reduces these PDEs into various ordinary differential equations and helps to find exact solutions of $$(2+1)$$ -dimensional KdV-Burgers equation. With the help of reduced equations, we have obtained the exact explicit solutions. Moreover, later by power series method, the exact analytic solutions of the KdV-Burgers equation are obtained.