Resumen
En este trabajo se obtiene una clasificación completa del grupo de simetrías de Lie para una generalización de la ecuación de Chazy, se calcula el grupo de equivalencia y se utiliza éste para presentar el álgebra principal de la ecuación.
Citas
A.A. Adam, F. M. Mahomed, Integration of Ordinary Differential Equations via Nonlocal Symmetries, Nonlinear Dynamics, Springer, Cham 30(2002), no. 3, 267–275. Doi: 10.1023/a:1020518129295
D.J. Arrigo, Symmetry Analysis of Differential Equations,Wiley (2014). Url: https://n9.cl/plyqs
T. Aziz, A. Fatima, C.M. Khalique, F.M. Mahomed, Prandtl’s boundary layer equation for two-dimensional flow: Exact solutions via the simplest equation method, Mathematical Problems in Engineering, Hindawi, 1(2013), no. 724385, 1–5. Doi: 10.1155/2013/724385
W.G. Bickley, LXXIII. The plane jet, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 23(1937), no. 156, 727–731. Doi: 10.1080/14786443708561847
G. Bluman, S. Anco, Symmetry and Integration Methods for Differential Equations, Springer, New York, (2002). Doi: 10.1007/b97380
G. Bluman, S. Anco, Symmetry and Integration Methods for Differential Equations, Springer, New York (2008). Doi: 10.1007/b97380
G.W. Bluman, A.F. Cheviakov, S.C. Anco, Applications of Symmetry Methods to Partial Differential Equations, Springer, New York (2010). Doi: 10.1007/978-0-387-68028-6
J.P. Boyd, The Blasius function: Computations before computers, the value of tricks, undergraduate projects, and open research problems, SIAM, Society for Industrial and Applied Mathematics, Philadelphia PA, 50(2008), no. 4, 791–804. Doi: 10.1137/070681594
K.P. Burr, T.R. Akylas, C.C. Mei, Chapter Two – Dimensional Laminar Boundary Layers, SIAM, Society for Industrial and Applied Mathematics, Philadelphia PA (2010). Accessed on 5-11-2021. Url: https://web.mit.edu/fluids-modules/www/highspeed_flows/ver2/bl_Chap2.pdf
J. Chazy, Sur les équations différentielles dont l’integrale générale est uniforme et admet des singularités essentielles mobiles, C. R. Acad. Sc. Paris 149(1909), no. 1, 563–565.
J. Chazy, Sur les équations différentielles du troisième ordre et d’ordre supérieur dont l’intégrale générale a ses points critiques fixes, Acta Mathematica, International Press of Boston 34(1962), no. 0, 317–385. Doi: 10.1007/bf02393131
P.A. Clarkson, P.J. Olver, Symmetry and the Chazy equation, Journal of Differential Equations, 124(1996), no. 1, 225–246. Doi: 10.1006/jdeq.1996.0008
M.B. Glauert, The wall jet, Journal of Fluid Mechanics, Cambridge University 1(1956), no. 6, 625. Doi: 10.1017/S002211205600041X
P.E. Hydon, Applications of Lie Groups to Differential Equations A Beginner’s Guide, Cambridge University Press (2000). Doi: 10.1017/CBO9780511623967
N.H. Ibragimov, M. Torrisi, A. Valenti, Preliminary group classification of equations vtt=f (x, vx)vxx + g(x; vx), Journal of Mathematical Physics, AIP Publishing 32(1991), no. 11, 2988. Doi: 10.1063/1.529042
N.H. Ibragimov, M. Torrisi, A simple method for group analysis and its application to a model of detonation, Journal of Mathematical Physics, AIP Publishing 33(1992), no. 11, 3931–3937. Doi: 10.1063/1.529841
N.H. Ibragimov, M.C. Nucci, Integration of third order ordinary differential equations by Lie’s method: Equations admitting three-dimensional Lie algebras, Lie Groups and their Applications 1(1994), no. 2, 49–64.
N.H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, CRC Press, Boca Raton FL (1995), Vol. 3. Url: https://n9.cl/jamtq
N.H. Ibragimov, N. Säfström, The equivalence group and invariant solutions of a tumour growth model, Communications in Nonlinear Science and Numerical Simulation, Elsevier 9(2004), no. 1, 61–68. Doi: 10.1016/s1007-5704(03)00015-7
G. Loaiza, Y. Acevedo, O.M.L. Duque, Álgebra óptima y soluciones invariantes para la ecuación de Chazy, Ingeniería y Ciencia, Eafit University, International Journal of Differential Equations, Hindawi, 17(2021), no. 33, 7–21. Doi: 10.17230/ingciencia.17.33.1
G. Loaiza, Y. Acevedo, O.M.L. Duque, D.A. García Hernández, Lie algebra classification, conservation laws, and invariant solutions for a generalization of the Levinson–Smith equation, International Journal of Differential Equations, 1(2021), no. 1, 1–11. Doi: 10.1155/2021/6628243
G. Loaiza, Y. Acevedo, O.M.L. Duque, D.A. García Hernández, 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, Universidad Industrial de Santander 39(2021), no. 2, 1–11. Doi: 10.18273/revint.v39n2-2021007
R. Naz, F M. Mahomed, D.P. Mason, Symmetry solutions of a thirdorder ordinary differential equation which arises from Prandtl boundary layer equations, Journal of Nonlinear Mathematical Physics, Atlantis Press 15(2008), no. sup 1, 179–191. Doi: 10.2991/jnmp.2008.15.s1.16
P.J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York (1986). Doi: 10.1007/978-1-4684-0274-2
L.V. Ovsiannikov, Group Analysis of Differential Equations, Nauka, Moscow, 1978. English transl., Academic Press, New York (1982).Url: https://www.elsevier.com/books/group-analysis-of-differentialequations/ovsiannikov/978-0-12-531680-4
N. Riley, Asymptotic expansions in radial jets, Journal of Mathematics and Physics, Wiley 41(1962), no. 1-4, 132–146. Doi: 10.1002/sapm1962411132
H. Schlichting, Laminare Strahlausbreitung, ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Wiley, 13(1933), no. 2, 260–263. Doi: 10.1002/zamm.19330130403
H.B. Squire, Radial Jets, Springer, Book: 50 Jahre Grenzschichtforschung (1955), 47–54. Doi: 10.1007/978-3-663-20219-6_5