Hamilton-Jacobi方程的对称约化和精确解

Symmetry Reductions and Exact Solutions of Hamilton-Jacobi Equations

对称群法是研究非线性偏微分方程对称约化和精确解的有效方法。本文利用广义条件对称方法研究容许二阶广义条件对称的Hamilton-Jacobi方程。对一些类型的Hamilton-Jacobi方程,我们得到了该类方程的对称约化和精确解。

The symmetry group related methods have been proven to be effective to study the sym-metry reductions and exact solutions of nonlinear partial differential equations.The conditional Lie-B¨acklund symmetry method is developed to study Hamilton-Jacobi equations which admit second order conditional Lie-Bcklund symmetries.For certain equations,symmetry reductions and exact solutions to the resulting equations are obtained.