二阶线性双曲型方程变换为常微分方程求解定理及应用  

The Solving Theorem that Second Order Linear Hyperbolic Equation Can Be Changed into Ordinary Differential Equation and Its Application

作　　者：刘许成[1] 

机构地区：[1]潍坊学院数学与信息科学学院,山东潍坊261061

出　　处：《大学数学》2012年第1期132-136,共5页College Mathematics

摘　　要：二个自变量的二阶线性双曲型方程auxx+2buxy+cuyy+dux+euy+g=0,当系数a,b,c,d,e,g满足一定条件时,可以利用变换T:ξ=φ(x,y),η=ψ(x,y)化为一阶线性常微分方程求解,本文给出了求解定理和计算方法.Abstract： To the second order linear hyperbolic equation with two independent variables auxx＋2buxy＋dux＋euy＋g=0 when its coefficients a ,b,c, d,e satisfy given conditions, we may utilize the transformation T：ξ=φ（x,y）,η=φ（x,y） to make it as first order linear ordinary differential equation for solving. At the same time, we give the discrimination theorem and application method.

关 键 词：二阶线性双曲型方程 特征线 特征方程 

分 类 号：O175.27[理学—数学]