Classification of Discrete Symmetries of Ordinary Differential Equations

Studies in Applied Mathematics

Volumn 111, Issue 3, 2003, Pages 269-299

  Laine Pearson, F E ^a   Hydon, P E ^a  

^a UNIVERSITY OF SURREY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

MATRIX ALGEBRA; TABLE LOOKUP;

AUTOMORPHISMS; CONSTANT MATRIX; DISCRETE POINTS; DISCRETE SYMMETRY; LIE ALGEBRA; LIE POINT SYMMETRIES; MATRIX; POINT SYMMETRY; POINT TRANSFORMATIONS; SIMPLE METHOD;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 0141636472     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9590.t01-1-00234     Document Type: Article

References (17)

1. M. GOLUBITSKY, I. STEWART, and D. G. SCHAEFFER, Singularities and Groups in Bifurcation Theory, Vol. II, Springer-Verlag, New York, 1988.
2. E. ALLGOWER, K. BÖHMER, and M. GOLUBITSKY (Eds.), Bifurcation and Symmetry, Birkhäuser, Basel, 1992.
3. J. M. CHADHAM, M. GOLUBITSKY, M. G. M. GOMES, E. KNOBLOCH, and I. N. STEWART (Eds.), Pattern Formation: Symmetry Methods and Applications, AMS, Providence RI, 1991.
4. P. A. CLARKSON and P. J. OLVER, Symmetry and the Chazy equation, J. Diff. Eqns. 124:225-246 (1996).
5. G. J. REID, D. T. WEIH, and A. D. WITTKOPF, A point symmetry group of a differential equation which cannot be found using infinitesimal methods, in Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics (N. H. Ibragimov, M. Torrisi, and A. Valenti, Eds.), pp. 311-316, Kluwer, Dordrecht, 1993.
6. G. GAETA and M. A. RODRÍGUEZ, Determining discrete symmetries of differential equations, Nuovo Cimento B 111:879-891 (1996).
7. P. E. HYDON, Symmetry Methods for Differential Equations, Cambridge University Press, Cambridge, 2000.
8. H. STEPHANI, Differential Equations: Their Solution Using Symmetries, Cambridge University Press, Cambridge, 1989.
9. P. J. OLVER, Applications of Lie Groups to Differential Equations (2nd ed.), Springer-Verlag, New York, 1993.
10. G. W. BLUMAN and S. KUMEI, Symmetries and Differential Equations, Springer-Verlag, New York, 1989.
11. A. GONZÁLEZ-LÓPEZ, N. KAMRAN, and P. J. OLVER, Lie algebras of vector fields in the real plane, Proc. Lond. Math. Soc. 64:339-368 (1992).
12. P. J. OLVER, Equivalence, Invariants and Symmetry, Cambridge University Press, Cambridge, 1995.
13. P. E. HYDON, Discrete point symmetries of ordinary differential equations, Proc. R. Soc. Lond. A 454:1961-1972 (1998).
14. WATERLOO MAPLE SOFTWARE, Maple V Release 5.1, Waterloo, Ontario, Canada, 1999.
15. P. E. HYDON, How to construct the discrete symmetries of partial differential equations, Eur. J. Appl. Math. 11:515-527 (2000).
16. P. E. HYDON, How to find discrete contact symmetries, J. Nonlin. Math. Phys. 5:405-416 (1998).
17. P. E. HYDON, How to use Lie symmetries to find discrete symmetries, in Modern Group Analysis VII (N. H. Ibragimov, K. R. Naqvi, and E. Straume, Eds.), pp. 141-147, MARS Publishers, Trondheim, 1999.