  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.
