A PROPERTY OF THE DEFINING EQUATIONS FOR THE LIE ALGEBRA IN THE GROUP CLASSIFICATION PROBLEM FOR WAVE EQUATIONS

被引：2

作者：

Khabirov, S. V. ^{[1
]}

机构：

[1] Russian Acad Sci, Inst Mech, Ufa Sci Ctr, Ufa 450001, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2009年 / 50卷 / 03期

关键词：

symmetries of differential equations; group classification; defining equations of the admissible Lie algebra;

D O I：

10.1007/s11202-009-0058-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We solve the group classification problem for nonlinear hyperbolic systems of differential equations. The admissible continuous group of transformations has the Lie algebra of dimension less than 5. This main statement follows from the principal property of the defining equations of the admissible Lie algebra: the commutator of two solutions is a solution. Using equivalence transformations we classify nonlinear systems in accordance with the well-known Lie algebra structures of dimension 3 and 4.

引用

页码：515 / 532

页数：18

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