热方程的非古典势对称群与不变解

基金项目: 国家自然科学基金资助项目(10272021)

Nonclassical Potential Symmetries and Invariant Solutions of Heat Equation

1.
School of Science, Chongqing Technology and Business University, Chongqing 400067, P. R. China;

摘要: 主要研究了热方程与波方程的非古典势对称群生成元及相应的群不变解．研究表明对于守恒形式的偏微分方程，可通过其伴随系统求得的非古典势对称群生成元来构造其显式解．这些显式解不能由方程本身的Lie对称群生成元或Lie-B?cklund对称群生成元构造得到．
- 非古典势对称群生成元 /
- 热方程 /
- 波方程 /
- 显式解
Abstract: Some nonclassical potential symmetry generators and group-invariant of heat equation and wave equation were determined. It is shown that new explicit solutions of conserved equations can be constructed by using the nonclassical potential symmetry generators which are derived from their adjoit system. These explicit solutions cannot be obtained by using the Lie or Lie-B_3/4 cklund symmetry group generators of differential equations.
- nonclassical potential symmetry generators /
- heat equation /
- wave equation /
- explicit solution

[1]	Olver P J.Applications of Lie Groups to Differential Equations[M].New York:Springer-Verlag,1996.
[2]	Ibragimov N H.Transformation Groups Applied to Mathematical Physics[M].New York:Springer-Verlag,1987.
[3]	Bluman G W,Kumei S.Symmetries and Differential Equations[M].New York:Springer-Verlag,1989.
[4]	Ovsiannikov L V.Group Analysis of Differential Equations[M].New York:Academic,1989.
[5]	Bluman G W,Cole J D.The general similarity solutions of the heat equation[J].Journal of Mathematics and Mechanics,1969,18(5):1025—1042.
[6]	Bluman G W,Kumei S.New classes of symmetries for partial differential equation[J].Journal of Mathematical Physics,1988,29(4):806—811. doi: 10.1063/1.527974
[7]	Johnpiliai A G,Kara A H.Nonclassical potential symmetry generators of differential equations[J].Nonlinear Dynamics,2002,30(2):167—177. doi: 10.1023/A:1020498600432
[8]	Gandaries M L.Nonclassical potential symmetries of the Burgers equation[A].In:Shkil M,Nikitin A,Boyko V Eds.Symmetry in Nonlinear Mathematical Physics[C].Vol 1.Klev:Institute of Mathematics of NAS of Ukraine,1997,130—137.