First integrals and reduction of a class of nonlinear higher order ordinary differential equations

Journal of Mathematical Analysis and Applications

Volumn 287, Issue 2, 2003, Pages 473-486

  Euler, N ^a   Leach, P G L ^b  

^a LULEÅ UNIVERSITY OF TECHNOLOGY   (Sweden)

^b UNIVERSITY OF KWAZULU NATAL   (South Africa)

Author keywords

First integrals; Integrability; Nonlinear ordinary differential equations

Indexed keywords

EID: 0346899422     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00544-4     Document Type: Article

References (19)

1. B. Abraham-Shrauner, A. Guo, Hidden symmetries associated with the projective group of nonlinear first order ordinary differential equations, J. Phys. A 25 (1992) 5597-5608.
2. K. Andriopoulos, P.G.L. Leach, G.P. Flessas, Complete symmetry groups of ordinary differential equations and their integrals: some basic considerations, J. Math. Anal. Appl. 262 (2001) 256-273.
3. W.E. Boyce, R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley, New York, 1969.
4. n = 0, J. Nonlinear Math. Phys. 4 (1997) 310-337.
5. N. Euler, T. Wolf, P.G.L. Leach, M. Euler, Linearisable third order ordinary differential equations and generalised Sundman transformations: The case X‴ = 0, Acta Appl. Math. 76 (2003) 89-115, nlin.SI/0203028.
6. G.P. Flessas, K.S. Govinder, P.G.L. Leach, Remarks on the symmetry Lie algebras of first integrals of scalar third order ordinary differential equations with maximal symmetry, Bull. Greek Math. Soc. 36 (1994) 63-79.
7. G.P. Flessas, K.S. Govinder, P.G.L. Leach, Characterisation of the algebraic properties of first integrals of scalar ordinary differential equations of maximal symmetry, J. Math. Anal. Appl. 212 (1997) 349-374.
8. K.S. Govinder, P.G.L. Leach, On the determination of nonlocal symmetries, J. Phys. A 28 (1995) 5349-5359.
9. n = 0, J. Math. Phys. 26 (1985) 2510-2514.
10. P.G.L. Leach, Analysis of an equation arising in general relativity, in: R. Vichnevetsky, J.J.H. Miller (Eds.), IMACS '91 Proceedings, Criterion, Dublin, 1991, pp. 363-364.
11. P.G.L. Leach, R. Maartens, S.D. Maharaj, Self-similar solutions of the generalized Emden-Fowler equation, Internat. J. Nonlinear Mech. 27 (1992) 575-582.
12. P.G.L. Leach, B. Abraham-Shrauner, K.S. Govinder, Symmetries of first integrals and their associated differential equations, J. Math. Anal. Appl. 235 (1999) 58-83.
13. P.G.L. Leach, S. Cotsakis, G.P. Flessas, Symmetry, singularity and integrability in complex dynamics: I. The reduction problem, J. Nonlinear Math. Phys. 7 (2000) 445-479.
14. P.G.L. Leach, R. Maartens, S.D. Maharaj, Self-similar solutions of the generalized Emden-Fowler equation, Internat. J. Nonlinear Mech. 27 (1992) 575-582.
15. F.M. Mahomed, P.G.L. Leach, Contact symmetries of second order differential equations, J. Math. Phys. 32 (1991) 2051-2055.
16. C.M. Mellin, F.M. Mahomed, P.G.L. Leach, Solution of generalized Emden-Fowler equations with two symmetries, Internat. J. Nonlinear Mech. 29 (1994) 529-538.
17. G.M. Mubarakzyanov, On solvable Lie algebras, Izv. Vyssh. Uchebn. Zaved. Mat. 32 (1963) 114-123.
18. G.M. Mubarakzyanov, Classification of real structures of five-dimensional Lie algebras, Izv. Vyssh. Uchebn. Zaved. Mat. 34 (1963) 99-106.
19. G.M. Mubarakzyanov, Classification of solvable six-dimensional Lie algebras with one nilpotent base element, Izv. Vyssh. Uchebn. Zaved. Mat. 35 (1963) 104-116.