In this paper we develop a systematic reduction procedure for determining intermediate integrals of second order hyperbolic equations so that exact solutions of the second order PDEs under interest can be obtained by solving first order PDEs. We give some conditions in order that such a procedure holds and, in particular, we characterize classes of linear second order hyperbolic equations for which the general solution can be found.

中文翻译：

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确定二阶双曲方程精确解的归约过程


在本文中，我们开发了一种系统化简程序，用于确定二阶双曲方程的中间积分，以便通过求解一阶偏微分方程可以获得感兴趣的二阶偏微分方程的精确解。我们给出了一些条件，以便这样的过程成立，特别是，我们描述了可以找到通解的线性二阶双曲方程的类别。