Nonlocal symmetries and solutions of the (2+1) dimension integrable Burgers equation

Abstract

The conservation laws of low-dimensional partial differential equations have been employed by Lou et al. to construct various high-dimensional equations, particularly focusing on high-dimensional integrable equations. However, solving these high-dimensional equations poses significant challenges. In this paper, the (2+1)-dimensional Burgers equation is studied by means of nonlocal symmetry method for the first time. For this high-dimensional equation, we establish a link with the exact solution of the (1+1)-dimensional Burgers equation through nonlocal symmetry. Furthermore, we successfully construct multiple exact solutions for the high-dimensional Burgers equation by leveraging the exact solution of the low-dimensional counterpart. We also give the corresponding images of several solutions to study the dynamic behavior of the equations.