Lie group classification of second-order ordinary difference equations
作者： Vladimir Dorodnitsyn , Roman Kozlov , Pavel Winternitz
DOI: 10.1063/1.533142
关键词:
摘要: A group classification of invariant difference models, i.e., equations and meshes, is presented. In the continuous limit results go over into Lie’s second-order ordinary differential equations. The discrete model a three point one we show that it can be under Lie groups dimension 0⩽n⩽6.
scitation.org
harvard.edu
aip.org
umontreal.ca 
sci-hub.se 参考文章(43)
Integrable systems, quantum groups, and quantum field theories Kluwer Academic. ,(1993) , 10.1007/978-94-011-1980-1
William F. Ames, Symmetries, exact solutions, and conservation laws CRC Press. ,(1994)
J. Krause, L. Michel, Classification of the symmetries of ordinary differential equations Group Theoretical Methods in Physics. ,vol. 382, pp. 251- 262 ,(1991) , 10.1007/3-540-54040-7_116
Giuseppe Gaeta, Nonlinear symmetries and nonlinear equations ,(1994)
Sophus Lie, Vorlesungen über continuierliche Gruppen mit geometrischen und anderen Anwendungen Chelsea Pub.. ,(1893)
V. Dorodnitsyn, P. Winternitz, Lie Point Symmetry Preserving Discretizations for Variable Coefficient Korteweg–de Vries Equations Nonlinear Dynamics. ,vol. 22, pp. 49- 59 ,(2000) , 10.1023/A:1008365224018
Peter J. Olver, Applications of Lie Groups to Differential Equations ,(1986)
R Hernández Heredero, D Levi, P Winternitz, Symmetries of the discrete Burgers equation Journal of Physics A. ,vol. 32, pp. 2685- 2695 ,(1999) , 10.1088/0305-4470/32/14/009
D. Gómez-Ullate, S. Lafortune, P. Winternitz, Symmetries of discrete dynamical systems involving two species Journal of Mathematical Physics. ,vol. 40, pp. 2782- 2804 ,(1999) , 10.1063/1.532728
Roberto Floreanini, Luc Vinet, Lie symmetries of finite‐difference equations Journal of Mathematical Physics. ,vol. 36, pp. 7024- 7042 ,(1995) , 10.1063/1.531205