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 Bcklund 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 Bcklund transformations.
基金
Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 10971018
the Natural Science Foundation of Shandong Province under Grant No.ZR2010AM029
the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province under Grant No.BS2010SF001
the Doctoral Foundation of Binzhou University under Grant No.2009Y01
