Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 39 Núm. 2 (2021): Revista Integración, temas de matemáticas
Artículos científicos

Sistema óptimo, soluciones invariantes y clasificación completa del grupo de simetrías de Lie para la ecuación de Kummer-Schwarz generalizada y su representación del álgebra de Lie

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  • Danilo García Hernández,
  • Oscar Mario Londoño Duque,
  • Yeisson Acevedo,
  • Gabriel Loaiza
Danilo García Hernández
IMEC-UNICAMP, Escola de matemática, Campinas, Brasil.
Oscar Mario Londoño Duque
IMEC-UNICAMP, Escola de matemática, Campinas, Brasil.
Yeisson Acevedo
Universidad EAFIT, Departamento de ciencias matemáticas, Medellín, Colombia.
Gabriel Loaiza
Universidad EAFIT, Departamento de ciencias matemáticas, Medellín, Colombia.
DOI: https://doi.org/10.18273/revint.v39n2-2021007

Publicado 2021-10-08

Palabras clave

  • Soluciones invariantes,
  • grupo de simetría de Lie,
  • Sistema optimal,
  • Clasificación del álgebra de Lie,
  • Ecuación de Kummer - Schwarz

Cómo citar

García Hernández, D., Londoño Duque, O. M., Acevedo, Y., & Loaiza, G. (2021). Sistema óptimo, soluciones invariantes y clasificación completa del grupo de simetrías de Lie para la ecuación de Kummer-Schwarz generalizada y su representación del álgebra de Lie. Revista Integración, Temas De matemáticas, 39(2), 257–274. https://doi.org/10.18273/revint.v39n2-2021007

Derechos de autor 2021 Revista Integración, temas de matemáticas

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.

Resumen

Obtenemos la clasificación completa del grupo de simetría de Lie y los operadores generadores del sistema optimal asociados a un caso particular de la ecuación de Kummer - Schwarz generalizada. Utilizando esos operadores, caracterizamos todas las soluciones invariantes, se encontraron soluciones alternativas para la ecuación estudiada y se clasifica el álgebra de Lie asociada al grupo de simetría.

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Referencias

  1. Ali M.R. and Sadat R., “Lie symmetry analysis, new group invariant for the (3 + 1) - dimensional and variable coefficients for liquids with gas bubbles models”, Chinese J. Phys., 71 (2021), 539–547. doi: 10.1016/j.cjph.2021.03.018.
  2. Alimirzaluo E., Nadjafikhah M. and Manafian J., “Some new exact solutions of (3 + 1) - dimensional burgers system via lie symmetry analysis”, Adv. Difference Equ., 2021 (2021), No. 1, 1–17. doi: 10.1186/s13662-021-03220-3.
  3. Bozhkov Y.D. and Ramos P., “On the generalizations of the Kummer-Schwarz equation”, Nonlinear Anal. Optim., 192 (2020), 111–691. doi: 10.1016/j.na.2019.111691.
  4. Bluman G. and Kumei S., Symmetries and Differential Equations, Springer Science & Business Media, vol. 81, New York, 1989.
  5. Bluman G. and Anco S., Symmetry and integration methods for differential equations, Springer Science & Business Media, vol. 154, New York, 2008.
  6. Bluman G., Cheviakov A. and Anco S., Applications of symmetry methods to partial differential equations, Springer, vol. 168, New York, 2010.
  7. Cariñena J.F. and De Lucas J., “Applications of lie systems in dissipative MilnePinney equations”, Int. J. Geom. Methods Mod. Phys., 6 (2009), No. 4, 683–699. doi: 10.1142/S0219887809003758.
  8. Cantwell B.J., Introduction to Symmetry Analysis, Cambridge University Press, Cambridge, 2002.
  9. Gainetdinova A.A., Ibragimov N.H. and Meleshko S.V., “Group classification of ODE y ′′′ = F(x, y, y′ )′′, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), No. 2, 345–349. doi: 10.1016/j.cnsns.2013.06.009.
  10. Ghose-Choudhury A. et al., “Noetherian symmetries of noncentral forces with drag term”, Int. J. Geom. Methods Mod. Phys., 14 (2017), No. 2, 1750018. doi: 10.1142/S0219887817500189.
  11. Gaeta G. and Spadaro F., Random Lie - point symmetries of stochastic differential equations, AIP Publishing LLC, 5th ed., vol. 58, 2017.
  12. Gibbons G.W., “Dark energy and the Schwarzian derivative”, arXiv:1403.5431.
  13. Hu W., et al., “Symmetry breaking of infinite-dimensional dynamic system”, Appl. Math. Lett., 103 (2020), 106–207. doi: 10.1016/j.aml.2019.106207.
  14. Hydon P.E., “Discrete point symmetries of ordinary differential equations”, Proc. R. Soc. Lond. Ser., 454 (1998), No. 1975, 1961–1972. doi: 10.1098/rspa.1998.0243.
  15. Hydon P.E. and Crighton D., Symmetry methods for differential equations: a beginner’s guide, Cambridge University Press, vol. 22, Cambridge, 2000.
  16. Humphreys J.E., Introduction to Lie algebras and representation theory, Springer-Verlag, 1st ed., vol. 9, New York, 2012.
  17. Hussain Z., Sulaiman M. and Sackey E., “Optimal system of subalgebras and invariant solutions for the Black-Scholes equation”, Thesis (MSc), Blekinge Institute of Technology, 2009, 69 p.
  18. Ibragimov N.H. and Nucci M.C., “Integration of Third Order Ordinary Differential Equations by Lie’s Method: Equations Admitting Three - Dimensional Lie Algebras”, Lie Groups Appl., 1 (1994), No. 2, 49–64.
  19. Ibragimov N.H., CRC Handbook of Lie Group Analysis of Differential Equations, CRC Press, vol. 3, 1995.
  20. Khudija B., “Particular solutions of ordinary differential equations using discrete symmetry groups”, Symmetry., 12 (2020), No. 1, 180. doi: 10.3390/sym12010180.
  21. Kumar S., Ma W. X. and Kumar A., “Lie symmetries, optimal system and group - invariant solutions of the (3+1) - dimensional generalized KP equation”, Chinese J. Phys., 69 (2021), 1–23. doi: 10.1016/j.cjph.2020.11.013.
  22. Kumar S., Kumar D. and Kumar A., “Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional fokas equation”, Chaos Solitons Fractals., 142 (2021), 110–507. doi: 10.1016/j.chaos.2020.110507.
  23. Kumar S., Kumar D. and Wazwaz A.M., “Lie symmetries, optimal system, group invariant solutions and dynamical behaviors of solitary wave solutions for a (3+1) dimensional KdV-type equation”, The European Physical Journal Plus., 136 (2021), No. 5, 1–36. doi: 10.1140/epjp/s13360-021-01528-3.
  24. Kumar S., Almusawa H. and Kumar A., “Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2 + 1)-dimensional rdDym equation using the lie symmetry approach”, Results in Physics., 24 (2021), 104–201. doi: 10.1016/j.rinp.2021.104201.
  25. Kumar D. and Kumar S., “Solitary wave solutions of pZK equation using Lie point symmetries” Eur. Phys. J. Plus., 135 (2020), No. 2, 1–19. doi: 10.1140/epjp/s13360-020-00218-w.
  26. Leach P.G, “Symmetry and singularity properties of the generalised KummerSchwarz and related equations”, J. Math. Anal., 348 (2008), No. 1, 487–493. doi: 10.1016/j.jmaa.2008.07.018.
  27. Leach P.G. and Paliathanasis A., “Symmetry analysis for a fourth-order noisereduction partial differential equation”, Quaest. Math., (2020), 1–12. doi: 10.2989/16073606.2020.1812009.
  28. Lie S., “Theorie der transformationsgruppen I”, Mathematische Annalen., 16 (1880), No. 4, 441–528. doi: 10.1007/BF01446218.
  29. Llibre J. and Vidal C., “Global dynamics of the Kummer-Schwarz differential equation”, Mediterr. J. Math., 11 (2014), No. 2, 477-486. doi: 10.1007/s00009-013-0299-4.
  30. Loaiza G., Acevedo Y., Duque O.M.L. and García D., “Lie algebra classification, conservation laws, and invariant solutions for a generalization of the Levinson-Smith equation”, Int. J. Differ. Equ., 2021 (2021), 1–11. doi: 10.1155/2021/6628243.
  31. Lu H. and Zhang Y., “Lie symmetry analysis, exact solutions, conservation laws and bäcklund transformations of the gibbons-tsarev equation”, arXiv:2002.11585.
  32. Mertens T.G., Turiaci G.J. and Verlinde H.L., “Solving the Schwarzian via the conformal bootstrap”, Journal High Energy Phys., 2017 (2017), No. 8, 1–57. doi: 10.1007/JHEP08(2017)136.
  33. Noether E., Invariante Variationsprobleme, Mathematisch-physikalische Klasse, 2nd ed., 1918.
  34. Ovsienko V. and Tabachnikov S., “What is the Schwarzian derivative”, Notices of the AMS., 56 (2009), No. 1, 34-36.
  35. Olver P.J., Applications of Lie Groups to Differential Equations, Springer-Verlag, 1st ed., vol. 107, New York, 1986.
  36. Ovsyannikov L., Group analysis of differential equations, Academic Press, 1st ed., New York, 1982.
  37. Paliathanasis A. and Leach P.G.L., “Symmetries and singularities of the Szekeres system”, Modern Phys. Lett. A., 381 (2017), No. 15, 1277–1280. doi: 10.1016/j.physleta.2017.02.009.
  38. Paliathanasis A., “Lie symmetry analysis and one-dimensional optimal system for the generalized 2+1 kadomtsev - petviashvili equation”, Physica Scripta., 95 (2020), No. 5, 055223. doi:10.1088/1402-4896/ab7a3a.
  39. Stephani H., Differential equations: Their solution using symmetries, Cambridge University Press, 1st ed., Cambridge, 1989.
  40. Tian S.F., “Lie symmetry analysis, conservation laws and solitary wave solutions to a fourth-order nonlinear generalized boussinesq water wave equation”, Appl. Math. Lett., 100 (2020), 106–156. doi: 10.1016/j.aml.2019.106056.
  41. Zaitsev V.F. and Polyanin A.D., Handbook of exact solutions for ordinary differential equations, Chapman and Hall/CRC, 2nd ed., New York, 2002.
  42. Zewdie G., “Lie simmetries of junction conditions for radianting stars”, Thesis (MSc), University of KwaZulu - Natal, Durban, 2011, 77 p.