The article presents a new method for constructing exact solutions of non-evolutionary partial differential equations with two independent variables. The method is applied to the linear classical equations of mathematical physics: the Helmholtz equation and the variable type equation. The constructed method goes back to the theory of finite-dimensional dynamics proposed for evolutionary differential equations by B. Kruglikov, O. Lychagina and V. Lychagin. This theory is a natural development of the theory of dynamical systems. Dynamics make it possible to find families that depends on a finite number of parameters among all solutions of PDEs. The proposed method is used to construct exact particular solutions of linear differential equations (Helmholtz equations and equations of variable type).

本文提出了一种构造具有两个自变量的非进化偏微分方程精确解的新方法。该方法适用于数学物理学上的线性经典方程：Helmholtz方程和可变类型方程。构造的方法可以追溯到B. Kruglikov，O。Lychagina和V. Lychagin为演化微分方程提出的有限维动力学理论。该理论是动力学系统理论的自然发展。通过动力学，可以在所有PDE解决方案中找到依赖于有限数量参数的族。所提出的方法用于构造线性微分方程（Helmholtz方程和可变类型方程）的精确特定解。