N-dimensional Auto-Bäcklund Transformation and Exact Solutions to n-dimensional Burgers System

Abstract

N-dimensional Bäcklund transformation (BT), Cole-Hopf transformation and Auto-Bäcklund transformation (Auto-BT) of n-dimensional Burgers system are derived by using simplified homogeneous balance (SHB). By the Auto-BT, another solution of the n-dimensional Burgers system can be obtained provided that a particular solution of the Burgers system is given. Since the particular solution of n-dimensional Burgers system can be given easily by the Cole-Hopf transformation, then using the Auto-BT repeatedly, more solutions of n-dimensional Burgers system can be obtained successively