二阶线性双曲型方程变换为常微分方程求解定理及应用

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.