Lie Algebra Representation, Conservation Laws and Some Invariant Solutions for a Generalized Emden-Fowler Equation
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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
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[2] S. Richardson, “The emission of electricity from hot bodies,” Nature, vol. 98, no. 146, 1916. https://doi.org/10.1038/098146a0
[3] 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.
[4] 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
[5] A. Polyanin and V. Zaitsev, Exact solutions for ordinary differential equations. Chapman and Hall/CRC, 2002.
[6] D. J. Arrigo, Symmetry analysis of differential equations. Wiley, (2014).
[7] 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.
[8] 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
[9] 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
[10] P. J. Olver, Applications of Lie Groups to Differential Equations. Springer-Verlag, (1986). https://doi.org/10.1007/978-1-4684-0274-2
[11] 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
[12] 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
[13] G. Zewdie, “Lie simmetries of junction conditions for radianting stars,” Master’s thesis, University of KwaZulu-Natal, (2011). http://hdl.handle.net/10413/9840
[14] E. Noether, “Problemas de variación invariante,” Gott. Nachr., vol. 2, pp. 235–257, 1918. https://doi.org/10.1080/00411457108231446
[15] 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
[16] I. Gelfand and S. Fomin, Calculus of Variations, ser. Dover Books on Mathematics. Dover Publications, 2012.
[17] J. Humphreys, Introduction to Lie Algebras and Representation Theory, ser. Graduate Texts in Mathematics. Springer New York, 2012.
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Published
Dec 1, 2021
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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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