Group properties of generalized quasi-linear wave equations

被引：10

作者：

Huang, Ding-jiang ^{[1
,2
,3
]}

Zhou, Shuigeng ^{[1
,2
]}

机构：

[1] Fudan Univ, Sch Comp Sci, Shanghai 200433, Peoples R China

[2] Fudan Univ, Shanghai Key Lab Intelligent Informat Proc, Shanghai 200433, Peoples R China

[3] E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 366卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Generalized quasi-linear wave equations; Group classification; Symmetry reduction; Nonclassical symmetries; Exact solutions; NONCLASSICAL SYMMETRY REDUCTIONS; GROUP CLASSIFICATION; NONLOCAL SYMMETRIES; NONLINEAR HEAT; SYSTEMS; TRANSFORMATIONS; INVARIANT; EXAMPLE;

D O I：

10.1016/j.jmaa.2010.01.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

in this paper. complete group classification of a class of (1 + 1)-dimensional generalized quasi-linear wave equations is performed by using the Lie-Ovsiannikov method. additional equivalent transformation and furcate split method. Lie reductions of some truly 'variable coefficient' wave equations which are singled out from the classification results are investigated. Some classes of exact solutions of these 'variable coefficient' wave equations are constructed by means of both the reductions and the additional equivalent transformations. The nonclassical symmetries to the generalized quasi-linear wave equation are also studied. This enabled to obtain some exact solutions of the wave equations which are invariant under certain conditional symmetries. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：460 / 472

页数：13

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