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Article

Noether, Partial Noether Operators and First Integrals for the Coupled Lane-Emden System

by
Ben Muatjetjeja
* and
Chaudry Masood Khalique
*
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2010, 15(3), 325-333; https://doi.org/10.3390/mca15030325
Published: 1 December 2010
Versions Notes

Abstract

Systems of Lane-Emden equations arise in the modelling of several physical phenomena, such as pattern formation, population evolution and chemical reactions. In this paper we construct Noether and partial Noether operators corresponding to a Lagrangian and a partial Lagrangian for a coupled Lane-Emden system. Then the first integrals with respect to Noether and partial Noether operators are obtained for the Lane-Emden system under consideration. We show that the first integrals for both the Noether and partial Noether operators are the same. However, the gauge function is different in certain cases.
Keywords: Lagrangian; Noether and partial Noether operators; First integrals; Lane- Emden system; Lie group methods Lagrangian; Noether and partial Noether operators; First integrals; Lane- Emden system; Lie group methods

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MDPI and ACS Style

Muatjetjeja, B.; Khalique, C.M. Noether, Partial Noether Operators and First Integrals for the Coupled Lane-Emden System. Math. Comput. Appl. 2010, 15, 325-333. https://doi.org/10.3390/mca15030325

AMA Style

Muatjetjeja B, Khalique CM. Noether, Partial Noether Operators and First Integrals for the Coupled Lane-Emden System. Mathematical and Computational Applications. 2010; 15(3):325-333. https://doi.org/10.3390/mca15030325

Chicago/Turabian Style

Muatjetjeja, Ben, and Chaudry Masood Khalique. 2010. "Noether, Partial Noether Operators and First Integrals for the Coupled Lane-Emden System" Mathematical and Computational Applications 15, no. 3: 325-333. https://doi.org/10.3390/mca15030325

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