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Conditional symmetries of nonlinear third-order ordinary differential equations
Symmetry analysis of a Lane-Emden-Klein-Gordon-Fock system with central symmetry
Centro de Matemática, Computação e Cognição, Universidade Federal do ABC-UFABC, Avenida dos Estados, 5001, Bairro Bangu, Santo André SP, 09.210-580, Brazil |
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, Republic of South Africa |
In this paper we introduce a sort of Lane-Emden system derived from the Klein-Gordon-Fock equation with central symmetry. Point symmetries are obtained and, since the system can be derived as the Euler-Lagrange equation of a certain functional, a Noether symmetry classification is also considered and conservation laws are derived from the point symmetries.
References:
[1] |
M. A. Abdulwahhab,
Nonlinear self-adjointness and conservation laws of Klein-Gordon-Fock equation with centra symmetry, Commun Nonlinear Sci Numer Simulat, 22 (2015), 1331-1340.
doi: 10.1016/j.cnsns.2014.07.025. |
[2] |
G. W. Bluman and S. Kumei,
Symmetries and Differential Equations, Springer, 1989.
doi: 10.1007/978-1-4757-4307-4. |
[3] |
Y. Bozhkov and A. C. G. Martins,
Lie point symmetries of the Lane-Emden systems, J. Math. Anal. Appl., 294 (2004), 334-344.
doi: 10.1016/j.jmaa.2004.02.022. |
[4] |
Y. Bozhkov and I. L. Freire,
Symmetry analysis of the bidimensional Lane-Emden systems, J. Math. Anal. Appl., 388 (2012), 1279-1284.
doi: 10.1016/j.jmaa.2011.11.024. |
[5] |
Y. Bozhkov and I. L. Freire,
On the Lane-Emden system in dimension one, Appl. Math. Comp., 218 (2012), 10762-10766.
doi: 10.1016/j.amc.2012.04.033. |
[6] |
S. Dimas and D. Tsoubelis,
SYM: A new symmetry-finding package for Mathematica, Proceedings of the 10th International Conference in Modern Group Analysis, Larnaca, Cyprus, 2004 (2004), 64-70.
|
[7] |
S. Dimas and D. Tsoubelis,
A New Heuristic Algorithm for Solving Overdetermined Systems of PDEs in Mathematica, in: 6th International Conference on Symmetry in Nonlinear Mathematical Physics, Kiev, Ukraine, 2005. |
[8] |
I. L. Freire, P. L. da Silva and M. Torrisi, Lie and Noether symmetries for a class of fourth-order Emden-Fowler equations, J. Phys. A: Math. Theor. , 46 (2013), 245206, 9 pp.
doi: 10.1088/1751-8113/46/24/245206. |
[9] |
I. S. Gradshteyn and I. M. Ryzhik,
Table of Integrals, Series, and Products, Seventh Edition, Academic Press, New York, 2007. |
[10] |
N. H. Ibragimov,
Elementary Lie Group Analysis and Ordinary Differential Equations, John Wiley and Sons, 1999. |
[11] |
B. A. Kochetov,
Lie group symmetries and Riemann function of Klein-Gordon-Fock equation with central symmetry, Commun Nonlinear Sci Numer Simulat, 19 (2014), 1723-1728.
doi: 10.1016/j.cnsns.2013.10.001. |
[12] |
T. E. Mogorosi, I. L. Freire, B. Muatjetjeja and C. M. Khalique,
Group analysis of a hyperbolic Lane-Emden system, Appl. Math. Comp., 292 (2017), 156-164.
doi: 10.1016/j.amc.2016.07.033. |
[13] |
B. Muatjetjeja and C. M. Khalique,
Lagrangian approach to a generalized coupled Lane-Emden system: Symmetries and first integrals, Commun Nonlinear Sci Numer Simulat, 15 (2010), 1166-1171.
doi: 10.1016/j.cnsns.2009.06.002. |
[14] |
B. Muatjetjeja and C. M. Khalique,
Lie group classification for a generalised coupled Lane-Emden system in one dimension, East. Asian. J. Appl. Math., 4 (2014), 301-311.
|
show all references
B. Muatjetjeja would like to thank the Faculty Research Committee of FAST, North-West University, Mafikeng Campus for their financial support.
References:
[1] |
M. A. Abdulwahhab,
Nonlinear self-adjointness and conservation laws of Klein-Gordon-Fock equation with centra symmetry, Commun Nonlinear Sci Numer Simulat, 22 (2015), 1331-1340.
doi: 10.1016/j.cnsns.2014.07.025. |
[2] |
G. W. Bluman and S. Kumei,
Symmetries and Differential Equations, Springer, 1989.
doi: 10.1007/978-1-4757-4307-4. |
[3] |
Y. Bozhkov and A. C. G. Martins,
Lie point symmetries of the Lane-Emden systems, J. Math. Anal. Appl., 294 (2004), 334-344.
doi: 10.1016/j.jmaa.2004.02.022. |
[4] |
Y. Bozhkov and I. L. Freire,
Symmetry analysis of the bidimensional Lane-Emden systems, J. Math. Anal. Appl., 388 (2012), 1279-1284.
doi: 10.1016/j.jmaa.2011.11.024. |
[5] |
Y. Bozhkov and I. L. Freire,
On the Lane-Emden system in dimension one, Appl. Math. Comp., 218 (2012), 10762-10766.
doi: 10.1016/j.amc.2012.04.033. |
[6] |
S. Dimas and D. Tsoubelis,
SYM: A new symmetry-finding package for Mathematica, Proceedings of the 10th International Conference in Modern Group Analysis, Larnaca, Cyprus, 2004 (2004), 64-70.
|
[7] |
S. Dimas and D. Tsoubelis,
A New Heuristic Algorithm for Solving Overdetermined Systems of PDEs in Mathematica, in: 6th International Conference on Symmetry in Nonlinear Mathematical Physics, Kiev, Ukraine, 2005. |
[8] |
I. L. Freire, P. L. da Silva and M. Torrisi, Lie and Noether symmetries for a class of fourth-order Emden-Fowler equations, J. Phys. A: Math. Theor. , 46 (2013), 245206, 9 pp.
doi: 10.1088/1751-8113/46/24/245206. |
[9] |
I. S. Gradshteyn and I. M. Ryzhik,
Table of Integrals, Series, and Products, Seventh Edition, Academic Press, New York, 2007. |
[10] |
N. H. Ibragimov,
Elementary Lie Group Analysis and Ordinary Differential Equations, John Wiley and Sons, 1999. |
[11] |
B. A. Kochetov,
Lie group symmetries and Riemann function of Klein-Gordon-Fock equation with central symmetry, Commun Nonlinear Sci Numer Simulat, 19 (2014), 1723-1728.
doi: 10.1016/j.cnsns.2013.10.001. |
[12] |
T. E. Mogorosi, I. L. Freire, B. Muatjetjeja and C. M. Khalique,
Group analysis of a hyperbolic Lane-Emden system, Appl. Math. Comp., 292 (2017), 156-164.
doi: 10.1016/j.amc.2016.07.033. |
[13] |
B. Muatjetjeja and C. M. Khalique,
Lagrangian approach to a generalized coupled Lane-Emden system: Symmetries and first integrals, Commun Nonlinear Sci Numer Simulat, 15 (2010), 1166-1171.
doi: 10.1016/j.cnsns.2009.06.002. |
[14] |
B. Muatjetjeja and C. M. Khalique,
Lie group classification for a generalised coupled Lane-Emden system in one dimension, East. Asian. J. Appl. Math., 4 (2014), 301-311.
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