Remarks on symmetry analysis of Lane-Emden systems of dimensions one and two
DOI:
https://doi.org/10.1590/S2179-84512013005000009Abstract
Some recent results on Lie group analysis of the one and bi-dimensional Lane-Emden systems are revisited.References
G. W. Bluman and S. Anco, “Symmetry and Integration Methods for Differential Equations’, Springer, New York, (2002).
G. W. Bluman and S. Kumei, “Symmetries and Differential Equations”, Applied Mathematical Sciences 81, Springer, New York, (1989).
Y. Bozhkov and A.C.G. Martins, Lie point symmetries of the Lane-Emden systems, J. Math. Anal. Appl., 294 (2004), 334-344
Y. Bozhkov and I. L. Freire, Symmetry analysis of the Lane-Emden systems in dimensions one and two, CNMAC, 2012.
Y. Bozhkov and I.L. Freire, Symmetry analysis of the bidimensional Lane-Emden systems, J. Math. Anal. Appl., 388 (2012), 1279-1284.
Y. Bozhkov and I.L. Freire, On the Lane-Emden system in dimension one, Appl.Math. Comp., 218 (2012), 10762-10766
Q. Dai and C. Tisdell, Nondegeneracy of positive solutions to homogeneous second-order differential systems and its applications, Acta Math. Sci. Ser., 29
(2009), 435-446
N. H. Ibragimov, “Transformation groups applied to mathematical physics”, Translated from the Russian Mathematics and its Applications (Soviet Series),
D. Reidel Publishing Co., Dordrecht, (1985).
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.
B. Muatjetjeja and C. M. Khalique, Noether, partial Noether operators and first integrals for the coupled Lane-Emden system, Mathematical and Computational
Applications, 15 (2010), 325 - 333.
B. Muatjetjeja and C. M. Khalique, First integrals for a generalized coupled Lane-Emden system, Nonlinear Anal. - Real World Applications, 12 (2011),
- 1212.
B. Muatjetjeja and C. M. Khalique, Conservation laws for a generalized coupled bidimensional Lane-Emden system, Commun. Nonlin. Sci. Num. Simil., DOI
1016/j.cnsns.2012.09.006, (2012).
P. J. Olver, “Applications of Lie groups to differential equations’, Springer, New York, (1986).
Downloads
Published
How to Cite
Issue
Section
License
Copyright
Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.
Intellectual Property and Terms of Use
The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.
The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.