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In this paper, the new (2+1)-dimensional Burgers equation has been derivedusing the Burgers equation' recursion operator as follows \begin{equation*}  u_{xt}+\left(u_{t}+uu_{x}-\nuu_{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 Burgersequation. Because of its complexity, we have applied the Lie symmetry approachto an equivalent equation of the new Burgers equation tom achieve 6-dimensionalvector fields of symmetry. The reduction process under four symmetriessubalgebras helps to investigate four simpler equations, one of which is thefamous Riccati equation. Therefore, four explicit solutions are attained andgraphically illustrated in 3D and countour plots. Different solitary wavedynamics are determined of the new (2+1)-dimensional Burgers equation, whichincludes bright soliton, breather, kink, periodic solution and someinteractions.

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