非线性d'Alembert方程的二维化
Reduction of non-linear d'Alembert equations to two-dimensional equations
摘要：
我们研究了多维波动方程（达朗贝尔方程和汉密尔顿方程的系统）的约化条件。我们证明了这样的系统的约化条件的相容性的必要条件。可能类型的减少方程代表有趣的类的二维抛物型，双曲型和椭圆型方程。用于d'Alembert（n维波）方程的约化的Ansatzes和方法也可以用于任意Poincare不变方程。这个看似简单而又局部的问题涉及到偏微分方程研究中的许多重要方面。
英文摘要：
We study conditions of reduction of the multidimensional wave equation - a system of the d'Alembert and Hamilton equations. We prove necessary conditions for compatibility of such system of the reduction conditions. Possible types of the reduced equations represent interesting classes of two-dimensional parabolic, hyperbolic and elliptic equations. Ansatzes and methods used for reduction of the d'Alembert (n-dimensional wave) equation can be also used for arbitrary Poincare-invariant equations. This seemingly simple and partial problem involves many important aspects in the studies of the PDE.
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