Symmetry classification of first integrals for scalar dynamical equations

被引：4

作者：

Mahomed, K. S. ^{[1
]}

Momoniat, E. ^{[1
]}

机构：

[1] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2014年 / 59卷

关键词：

First integrals; Symmetry; Non-linear ordinary differential equations; Emden-Fowler; Lane-Emden; Modified Emden; LIE-ALGEBRAS; EMDEN;

D O I：

10.1016/j.ijnonlinmec.2013.11.002

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We completely classify the first integrals of scalar non-linear second-order ordinary differential equations (ODEs) in terms of their Lie point symmetries. This is performed by first obtaining the classifying relations between point symmetries and first integrals of scalar non-linear second-order equations which admit one, two and three point symmetries. We show that the maximum number of symmetries admitted by any first integral of a scalar second-order non-linear ODE is one which in turn provides reduction to quadratures of the underlying dynamical equation. We provide physical examples of the generalized Emden-Fowler, Lane-Emden and modified Emden equations. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：52 / 59

页数：8

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