Lie Symmetry Analysis, Backlund Transformations and Exact Solutions to (2+1)-Dimensional Burgers' Types of Equations

摘要

This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations. All of the geometic vector fields of the equations are obtained, an optimal system of the equation is presented. Especially, the Mcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry. Then, all of the symmetry reductions are provided in terms of the optimal system method, and the exact explicit solutions are investigated by the symmetry reductions and Backlund transformations.