Partial Noether operators and first integrals via partial Lagrangians

被引:50
作者
Kara, A. H.
Mahomed, F. M. [1 ]
Naeem, I.
Soh, C. Wafo
机构
[1] Univ Witwatersrand, Sch Computat & Appl Math, Ctr Differential Equat Contiuum Mech & Appl, ZA-2050 Wits, South Africa
[2] Univ Witwatersrand, Sch Math, Ctr Differential Equat Contiuum Mech & Appl, ZA-2050 Wits, South Africa
[3] Jackson State Univ, Coll Sci Engn & Technol, Dept Math, Jackson, MS 39217 USA
关键词
ordinary differential equations; conservation laws;
D O I
10.1002/mma.939
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The notions of partial Lagrangians, partial Noether operators and partial Euler-Lagrange equations are used in the construction of first integrals for ordinary differential equations that need riot be derivable from variational principle; We obtain a Noether-like theorem that provides the first integral by means of a formula which ha the same structure as the Noether integral, However, the invariatice condition for the determination of the partial Noether operators is different as we have a partial Lagrangian and as a result partial Euler-Lagrange equations. Applications given include those that admit a standard Lagrangian such as the harmonic oscillator, modified Emden and Ermakov-Pinney equations and systems of two second-order equations that do not have standard Lagrangians. Copyright (c) 2007 John Wiley & Sons, Ltd.
引用
收藏
页码:2079 / 2089
页数:11
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