Symmetry Classifications and Reductions of (2+1)-dimensional Potential Burgers Equation

Abstract

We discuss the symmetries and reductions of the two-dimensional Potential Burgers Equation. We classify the one- and two-dimensional subalgebras of the symmetry algebra which is infinite-dimensional into conjugacy classes under the adjoint action of the symmetry group. Invariance under one-dimensional subalgebras provides the reductions to lower-dimensional partial differential equations (PDEs). Further reductions of these PDEs to second order ordinary differential equations (ODEs) are obtained through invariance under two dimensional subalgebras.