Complete group classification of systems of two linear second-order ordinary differential equations: the algebraic approach

被引：10

作者：

Mkhize, T. G. ^{[1
,2
]}

Moyo, S. ^{[3
,4
]}

Meleshko, S. V. ^{[5
]}

机构：

[1] Durban Univ Technol, Dept Math, ZA-4000 Durban, South Africa

[2] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, ZA-4000 Durban, South Africa

[3] Durban Univ Technol, Dept Math, ZA-4000 Durban, South Africa

[4] Durban Univ Technol, Inst Syst Sci, ZA-4000 Durban, South Africa

[5] Suranaree Univ Technol, Inst Sci, Sch Math, Nakhon Ratchasima 30000, Thailand

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2015年 / 38卷 / 09期

关键词：

group classification; linear equations; admitted Lie group; equivalence transformation; CONSTANT-COEFFICIENTS; SYMMETRY-BREAKING; ODES;

D O I：

10.1002/mma.3193

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a complete group classification of the general case of linear systems of two second-order ordinary differential equations. The algebraic approach is used to solve the group classification problem for this class of equations. This completes the results in the literature on the group classification of two linear second-order ordinary differential equations including recent results which give a complete group classification treatment of such systems. We show that using the algebraic approach leads to the study of a variety of cases in addition to those already obtained in the literature. We illustrate that this approach can be used as a useful tool in the group classification of this class of equations. A discussion of the subsequent cases and results is given. Copyright (c) 2014 John Wiley & Sons, Ltd.

引用

页码：1824 / 1837

页数：14

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