New (2+1)-dimensional Burgers equation and its solitary wave solutions via the Lie symmetry method

Abstract

In this paper, the new (2+1)-dimensional Burgers equation has been derived using the Burgers equation' recursion operator as follows \begin{equation*} u_{xt}+\left(u_{t}+uu_{x}-\nu u_{xx}\right)_{y}+3\left(u_{x}\partial_{x}^{-1}u_{y}\right)_{x}=0 \end{equation*} This nonlinear model is an interesting generalization of the Burgers equation. Because of its complexity, we have applied the Lie symmetry approach to an equivalent equation of the new Burgers equation tom achieve 6-dimensional vector fields of symmetry. The reduction process under four symmetries subalgebras helps to investigate four simpler equations, one of which is the famous Riccati equation. Therefore, four explicit solutions are attained and graphically illustrated in 3D and countour plots. Different solitary wave dynamics are determined of the new (2+1)-dimensional Burgers equation, which includes bright soliton, breather, kink, periodic solution and some interactions.