Lie Algebra Representation, Conservation Laws and Some Invariant Solutions for a Generalized Emden-Fowler Equation

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DOI:

https://doi.org/10.17230/ingciencia.17.34.5

Keywords:

Invariant solutions, Lie symmetry group, Optimal system, Lie algebra classification, variational simmetries, Conservation laws

Abstract

All generators of the optimal algebra associated with a generalization of the Endem-Fowler equation are showed; some of them allow to give invariant solutions. Variational symmetries and the respective conservation laws are also showed. Finally, a representation of Lie symmetry algebra is showed by groups of matrices.

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References

S. Chandrasekhar, An introduction to the study of stellar structure. Dover Publications, (1967).

S. Richardson, “The emission of electricity from hot bodies,” Nature, vol. 98, no. 146, 1916. https://doi.org/10.1038/098146a0

B. Mehta and R. Aris, “A note on a form of the emden-fowler equation,” Journal of Mathematical Analysis and Applications, vol. 36, no. 3, pp. 611–621, 1971.

A. V. Rosa, “Modelagem matemática e simulacao do núcleo morto en catali-sadores porosos para reacoes de ordens fracionárias,” Master’s thesis, Faculdade de engenharia química de Lorena, 2005. https://sistemas.eel.usp.br/bibliotecas/antigas/2005/EQD05002.pdf

A. Polyanin and V. Zaitsev, Exact solutions for ordinary differential equations. Chapman and Hall/CRC, 2002.

D. J. Arrigo, Symmetry analysis of differential equations. Wiley, (2014).

G. Loaiza, Y. Agudelo, and O. Duque, “Lie group symmetries complete classification for a generalized chazy equation and its equivalence group,” Revista de matemática: teoría y aplicaciones, vol. 29, no. 1, 2022.

G. Loaiza, Y. Acevedo, O. Duque, and D. García, “Lie algebra classification, conservation laws, and invariant solutions for a generalization of the levinson smith equation,” International Journal of Differential Equations, vol. 2021, pp. 1–11, 2021. https://doi.org/10.1155/2021/6628243

O. Duque, D. García, G. Loaiza, and Y. Acevedo, “Optimal system, reductions and lie algebra classification for kudryashov sinelshchikov equations of second order,” Examples and Counterexamples, vol. 1, p. 100033, 2021. https://doi.org/10.1016/j.exco.2021.100033

P. J. Olver, Applications of Lie Groups to Differential Equations. Springer-Verlag, (1986). https://doi.org/10.1007/978-1-4684-0274-2

P. E. Hydon, Symmetry Methods for Differential Equations: A Beginner’s Guide, ser. Cambridge Texts in Applied Mathematics. Cambridge University Press, 2000. https://doi.org/10.1017/CBO9780511623967

H. Zahid, S. Muhammad, and S. Edward, “Optimal system of subalgebras and invariant solutions for the Black-Scholes equation,” Master’s thesis, Blekinge Institute of Technology, (2009). https://www.diva-portal.org/smash/get/diva2:830112/FULLTEXT01.pdf

G. Zewdie, “Lie simmetries of junction conditions for radianting stars,” Master’s thesis, University of KwaZulu-Natal, (2011). http://hdl.handle.net/10413/9840

E. Noether, “Problemas de variación invariante,” Gott. Nachr., vol. 2, pp. 235–257, 1918. https://doi.org/10.1080/00411457108231446

M. Nucci and P. Leach, “An old method of jacobi to find lagrangians,” Journal of Nonlinear Mathematical Physics, vol. 16, no. 4, pp. 431–441, 2009. https://doi.org/10.1142/S1402925109000467

I. Gelfand and S. Fomin, Calculus of Variations, ser. Dover Books on Mathematics. Dover Publications, 2012.

J. Humphreys, Introduction to Lie Algebras and Representation Theory, ser. Graduate Texts in Mathematics. Springer New York, 2012.

Emden-Fowler equation

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Published

2021-12-01

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How to Cite

Loaiza Ossa, G. I., Acevedo-Agudelo, Y., Londoño-Duque, O., & García Hernández, D. A. (2021). Lie Algebra Representation, Conservation Laws and Some Invariant Solutions for a Generalized Emden-Fowler Equation. Ingeniería Y Ciencia, 17(34), 97-113. https://doi.org/10.17230/ingciencia.17.34.5

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