Abstract
We find all systems of first-order quadratic autonomous two-dimensional difference equations which have two linear Lie symmetries. Knowledge of these symmetries permits the systems to be integrated by a reduction procedure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ablowitz, M. J., and Ladik, F. J. (1976).Studies in Applied Mathematics,55, 213.
Ablowitz, M. J., and Ladik, F. J. (1977).Studies in Applied Mathematics,57, 1.
Date, E., Jimbo, M., and Mika, T. (1982).Journal of the Physical Society of Japan,51, 4116.
Gardini, L., Lupini, R., Mammana, C., and Messia, M. G. (1987).SIAM Journal of Applied Mathematics,47, 455.
Grammaticos, B., Ramani, A., and Papageorgiu, V. (1991).Physical Review Letters,67, 1825.
Hénon, M. (1976).Communications in Mathematical Physics,50, 69.
Hirota, R. (1979).Journal of the Physical Society of Japan,46, 312.
MacMillan, E. M. (1971). InTopics in Modern Physics, W. E. Brittin and H. Odabasi, eds., Colorado Associated Universities Press, Boulder, Colorado, p. 219.
Maeda, S. (1987),IMA Journal of Applied Mathematics,38, 129.
Quispel, G. R. W., and Sahadevan, R. (1993).Physics Letters A,184, 64.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Almeida, M.A., Santos, F.C. & Moreira, I.C. Lie symmetries of quadratic two-dimensional difference equations. Int J Theor Phys 36, 551–558 (1997). https://doi.org/10.1007/BF02435748
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02435748