一维齐次波动方程Cauchy问题达朗贝尔公式的另一种推导

Another Deduction about the Cauchy Problem of One-dimensional Homogeneous Wave Equation

主要针对齐次波动方程Cauchy问题的通解求解,也就是达朗贝尔公式的推导。大部分文献通过求出特征方程,进而得到达朗贝尔公式,利用方程的算子形式将齐次波动方程方程转化为常微分方程组,通过对两个常微分方程利用特征线法求解,同样能够得到达朗贝尔公式。

In this paper, we focus on the general solution of homogeneous wave equation, the way we get the D＇ Alembert＇ s formula. The formula can be obtained by the method of the characteristic equation by using the method of operator, we reform the equations into ordinary differential equations, then the D＇ Alembert＇ s formula can be derived in another way as well.