Dynamics and exact solutions of non-evolutionary partial differential equations

被引：2
|
作者：
Kushner, Alexei G. [1 ,2 ]
Matviichuk, Ruslan, I [1 ]
机构：
[1] Lomonosov Moscow State Univ, GSP 2, Moscow, Russia
[2] Moscow Pedag State Univ, M Pirogovskaya Str 1-1, Moscow 119991, Russia
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2021年 / 76卷
基金：
俄罗斯基础研究基金会;
关键词：
Helmholtz equation; Mixed type equations; Finite-dimensional dynamics; Symmetry; Exact solutions; Geometry of differential equations;
D O I：
10.1016/j.difgeo.2021.101761
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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). (c) 2021 Elsevier B.V. All rights reserved.
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页数：12
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