The Determination of Nonlocal Symmetries by the Technique of Reduction of Order

Journal of Mathematical Analysis and Applications

Volumn 251, Issue 2, 2000, Pages 871-884

  Nucci, M C ^a   Leach, P G L ^b,c  

^a UNIVERSITY OF PERUGIA   (Italy)

^b UNIVERSITY OF THE AEGEAN   (Greece)

^c UNIVERSITY OF KWAZULU NATAL   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034668454     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7141     Document Type: Article

References (16)

1. Abraham-Shrauner B., Leach P. G. L. Hidden symmetries of nonlinear ordinary differential equations. Allgower E., George K., Miranda R., "Exploiting Symmetry in Applied and Numerical Analysis". Lecture Notes in Applied Mathematics. 29:1993;1-10 Amer. Math. Soc. Providence.
2. Fowler R. H. The form near infinity of real, continuous solutions of a certain differential equation of the second order. Quart. J. Math. 45:1914;289-350.
3. Fowler R. H. The solutions of Emden's and similar differential equations. MNRAS. 91:1930;63-91.
4. C. Géromini, M. R. Feix, and, P. G. L. Leach, Exponential nonlocal symmetries and nonnormal reduction of order, preprint, MAPMO, Département mathématiques, Université d'Orléans, Orléans la Source, 45067 Orléans Cedex 2, France, 1997.
5. Govinder K. S., Leach P. G. L. On the determination of nonlocal symmetries. J. Phys. A. 28:1995;5349-5359.
6. Govinder K. S., Leach P. G. L. The nature and uses of symmetries of ordinary differential equations. South African J. Sci. 92:1996;23-28.
7. Head A. K. LIE, a PC program for Lie analysis of differential equations. Comput. Phys. Comm. 77:1993;241-248.
8. Krause J. On the complete symmetry group of the classical Kepler system. J. Math. Phys. 35:1994;5734-5748.
9. Leach P. G. L. An exact invariant for a class of time-dependent anharmonic oscillators with cubic anharmonicity. J. Math. Phys. 22:1981;465-470.
10. Leach P. G. L. Analysis of an equation arising in general relativity. Vichnevetsky R., Miller J. J. H., IMACS '91 Proceedings. 1991;pp-364 Criterion Press, Dublin.
11. Leach P. G. L., Maartens R., Maharaj S. D. Self-similar solutions of the generalised Emden-Fowler equation. Internat. J. Nonlinear Mech. 27:1992;575-582.
12. I. de C. Moreira, Comments on A Direct Approach to Finding Exact Invariants for One-Dimensional Time-Dependent Classical Hamiltonians', Research Report, IF/UFRJ/83/25, Universidade Federal do Rio de Janiero, Instituto de Física, Cidade Universitaria, Ilha do Fundaõ, Rio de Janiero, CEP: 21,944-RJ, Brazil, 1983.
13. Nucci M. C. Interactive REDUCE programs for calculating Lie point, non-classical, Lie-Bäcklund, and approximate symmetries of differential equations: Manual and floppy disk. Ibragimov N. H., CRC Handbook of Lie Group Analysis of Differential Equations. Vol. III. New Trends. 1996;415-481 CRC Press, Boca Raton.
14. Nucci M. C. The complete Kepler group can be derived by Lie group analysis. J. Math. Phys. 37:1996;1772-1775.
15. M. C. Nucci, and, P. G. L. Leach, The harmony in the Kepler and related problems, preprint, RT 2000-12, Dipartimento di Matematica e Informatica, Università di Perugia, 06123 Perugia, Italy, 2000.
16. Sherring J., Head A. K., Prince G. E. Dimsym and LIE: Symmetry determining packages. Math. Comput. Modelling. 25:1997;153-164.