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

Main Article Content

Gabriel Ignacio Loaiza Ossa
Yeisson Acevedo-Agudelo
Oscar Londoño-Duque
Danilo A. García Hernández


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


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.


Download data is not yet available.
Abstract 62 | PDF Downloads 31


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

[2] S. Richardson, “The emission of electricity from hot bodies,” Nature, vol. 98, no. 146, 1916.

[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.

[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.

[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.

[10] P. J. Olver, Applications of Lie Groups to Differential Equations. Springer-Verlag, (1986).

[11] P. E. Hydon, Symmetry Methods for Differential Equations: A Beginner’s Guide, ser. Cambridge Texts in Applied Mathematics. Cambridge University Press, 2000.

[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).

[13] G. Zewdie, “Lie simmetries of junction conditions for radianting stars,” Master’s thesis, University of KwaZulu-Natal, (2011).

[14] E. Noether, “Problemas de variación invariante,” Gott. Nachr., vol. 2, pp. 235–257, 1918.

[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.

[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.

Most read articles by the same author(s)