李群方法对一阶偏微分方程的应用

Duffing equation [J]. Int. J. Non-Linear Mechanics, 1992, 30(6): 783-792. The Application of Lie Group Method to First Order Partial Differential Equations

本文以李群为工具，给出了一种将一阶非线性偏微分方程化简为一阶拟线性方程或可积的一阶拟线性方程的方法．该方法可用于某些两个自变元的，接受一个或两个李群的一阶非线性偏微分方程，特别可用于某些单自由度Ｌａｇｒａｎｇｅ系统的Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ方程的求解．

A way of transforming first order nonlinear PDE to first order quasilinear PDE or integrable first order PDE by using Lie group method is presented. The presented way can be applied to some first order nonlinear PDE's which admit one or two Lie groups and have two independent variables,especially to Hamilton-Jacobi equations of some Lagrange systems which have one degree of freedom.