The characterization of third order ordinary differential equations admitting a transitive fiber-preserving point symmetry group

Journal of Mathematical Analysis and Applications

Volumn 206, Issue 2, 1997, Pages 364-388

  Grebot, Guy ^a  

^a UNIVERSITY OF BRASILIA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

LINEARIZATION; MATHEMATICAL TECHNIQUES; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS;

CANONICAL EQUATION; THIRD ORDER ORDINARY DIFFERENTIAL EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 0031062032     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5219     Document Type: Article

References (13)

1. 1. A. V. Bocharov, V. V. Sokolov, and S. I. Svinolupov, On some equivalence problems for differential equations, preprint, 1993.
2. 2. S. S. Chern, The geometry of a differential equation Y‴ = F(X,Y,Y′,Y′), Tensor (N.S.) 28 (1940), 173-176.
3. 3. R. Gardner, "The Method of Equivalence and Its Applications," SIAM, Philadelphia, 1989.
4. 4. O. Gat, Symmetry algebras of third-order ordinary differential equations, J. Math. Phys. 33 No. 9 (1992), 2966-2971.
5. 5. G. Grebot, "On Killing Tensors in Vacuum Space-Times and The Classification of Third Order Ordinary Differential Equations," Ph.D. Thesis, Queen Mary College, London, 1995.
6. 6. G. Grebot, The classification of third order ordinary differential equation, in "Proceedings of the CATHODE Workshop, Nijmegen, January 9-12, 1995," p. 23.
7. 7. M. Gregus, "Third Order Linear Differential Equations, Mathematics and Its Applications," Reidel, Dordrecht, Holland, 1987.
8. 8. L. Hsu and N. Kamran, Classification of second-order differential equations admitting Lie groups of fiber-preserving point symmetries, Proc. London Math. Soc. (3) 58, No. 2 (1989), 387-416.
9. 9. N. Kamran, Contributions to the study of the equivalence problem of Elie Cartan and its applications to partial ordinary differential equations, Mem. Cl. Sci. Acad. Roy. Belg. 45, No. 7 (1989).
10. 10. J. Krause and L. Michel, Équations différentielles linéaires d'ordre n > 2 ayant une algèbre de Lie de Symétrie de dimension n + 4, C. R. Acad. Sci. Paris Sér. I 307 (1988), 905-910.
11. 11. E. Laguerre, Sur les équations différentielles linéaires du troisième ordre, C. R. Acad. Sci. Paris 88 (1879), 116-119.
12. 12. F. M. Mahomed and P. G. L. Leach, Symmetry Lie algebras of nth order ordinary differential equations, J. Math. Anal. Appl. 151 (1990), 80-107
13. 13. S. Sternberg, "Lectures on Differential geometry," Prentice Hall, Englewood Cliffs, NJ, 1964.