Fokker Planck方程的非古典势对称群及新显式解

本文利用一种新方法对Fokker- Planck方程的非古典势对称群生成元进行研究,找到方程的几个非古典势对称群生成元,并采用非古典对称群方法由这些对称群生成元构造得到Fokker- Planck方程的相应显式解.这些新显式解不能由Fokker -Planck方程本身的Lie对称或Li-e B cklund对称来获得.在验证所求得显式解的过程中,还发现并得到了另外几个显式解.这些新显式解则不能由Fokker -Planck方程本身的Lie对称,Lie- B cklund对称或非古典势对称来获得.文章表明,通过偏微分方程的非古典势对称群生成元来寻找其显式解是可能的.

Nonclassical potential symmetries and new explicit solutions of Fokker-Planck equation

Nonclassical potential symmetries of Fokker Planck equation are determined by using a new method,and some class of new explicit solutions, which can not be obtained through the Lie symmetries or Lie Backlund symmetries of Fokker Planck equation, are constructed by using nonclassical symmetry method to these new symmetry generators. In the process of verification, more explicit solutions, which can not be derived from the Lie symmetries, Lie Backlund symmetries or Nonclassical potential symmetries of Fokker Planck equation,are found. It's shown that there is possibility of finding new explicit solutions of partial differential equations through their nonclassical potential symmetries.