Remarks on symmetry analysis of Lane-Emden systems of dimensions one and two

Igor Leite Freire

Abstract


Some recent results on Lie group analysis of the one and bi-dimensional Lane-Emden systems are revisited.

Full Text:

PDF

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).




DOI: https://doi.org/10.1590/S2179-84512013005000009

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.


Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

         

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia