# Noether Symmetries of a Generalized Coupled Lane-Emden-Klein-Gordon-Fock System with Central Symmetry

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Complete Noether Symmetries Analysis

**Lemma**

**1.**

**Proof.**

**Theorem**

**1.**

**Theorem**

**2.**

**Theorem**

**3.**

**Theorem**

**4.**

**Theorem**

**5.**

**Remark**

**1.**

## 3. Concluding Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Muatjetjeja, B. Coupled Lane-Emden-Klein-Gordon-Fock system with central symmetry: Symmetries and Conservation laws. J. Differ. Equ.
**2017**, 263, 8322–8328. [Google Scholar] [CrossRef] - Freire, I.L.; Muatjetjeja, B. Symmetry analysis of a Lane-Emden-Klein-Gordon-Fock system with central symmetry. Discret. Contin. Dyn. Syst. Ser. A
**2018**, 11, 667–673. [Google Scholar] [CrossRef] - Muatjetjeja, B.; Mogorosi, T.E. Variational principle and conservation laws of a generalized hyperbolic Lane-Emden system. J. Comput. Nonlinear Dyn.
**2018**, 13, 121002. [Google Scholar] [CrossRef] - Mogorosi, T.E.; Freire, I.L.; Muatjetjeja, B.; Khalique, C.M. Group anylsis of a hyperbolic Lane-Emden system. Appl. Math. Comput.
**2017**, 292, 156–164. [Google Scholar] - Mbusi, S.O.; Muatjetjeja, B.; Adem, A.R. Lie group classification of a generalized coupled Lane-Emden-Klein-Gordon-Fock system with central symmetry. Nonlinear Dyn. Syst. Theory
**2019**, 19, 186–192. [Google Scholar] - Bozhkov, Y.; Freire, I.L. Symmetry analysis of the bidimensional Lane-Emden system. J. Math. Anal. Appl.
**2012**, 388, 1279–1284. [Google Scholar] [CrossRef] - Muatjetjeja, B.; Khalique, C.M. Conservation laws for a generalized coupled bidimensional Lane-Emden system. Commun. Nonlinear Sci. Numer. Simulat.
**2013**, 18, 851–857. [Google Scholar] [CrossRef] - Noether, E. Invariante Variationsprobleme. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse
**1918**, 2, 235–257. [Google Scholar] - Bozhkov, Y.; Martins, A.C.G. Lie point symmetries of the Lane-Emden system. J. Math. Anal. Appl.
**2004**, 294, 334–344. [Google Scholar] [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Muatjetjeja, B.; Mbusi, S.O.; Adem, A.R.
Noether Symmetries of a Generalized Coupled Lane-Emden-Klein-Gordon-Fock System with Central Symmetry. *Symmetry* **2020**, *12*, 566.
https://doi.org/10.3390/sym12040566

**AMA Style**

Muatjetjeja B, Mbusi SO, Adem AR.
Noether Symmetries of a Generalized Coupled Lane-Emden-Klein-Gordon-Fock System with Central Symmetry. *Symmetry*. 2020; 12(4):566.
https://doi.org/10.3390/sym12040566

**Chicago/Turabian Style**

Muatjetjeja, B., S. O. Mbusi, and A. R. Adem.
2020. "Noether Symmetries of a Generalized Coupled Lane-Emden-Klein-Gordon-Fock System with Central Symmetry" *Symmetry* 12, no. 4: 566.
https://doi.org/10.3390/sym12040566