Symmetries of discrete dynamical systems

被引：68
作者：
Levi, D
Winternitz, P
机构：
[1] IST NAZL FIS NUCL,I-00185 ROME,ITALY
[2] UNIV MONTREAL,CTR RECH MATH,MONTREAL,PQ H3C 3J7,CANADA
来源：
JOURNAL OF MATHEMATICAL PHYSICS | 1996年 / 37卷 / 11期
关键词：
D O I：
10.1063/1.531722
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Differential-difference equations of the form u(n)=F-n(t,u(n-1),u(n),u(n+1)) are classified according to their continuous Lie point symmetry groups. It is shown that for nonlinear equations, the symmetry group can be at most seven-dimensional. The integrable Toda lattice is a member of this class and has a four-dimensional symmetry group. (C) 1996 American Institute of Physics.
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页码：5551 / 5576
页数：26
相关论文
共 34 条
[1]  
[Anonymous], MATH JAPONICA
[2]  
Bluman G. W., 1989, Symmetries and Differential Equations
[3]   QUASISOLITONS ON A DIATOMIC CHAIN AT ROOM-TEMPERATURE [J].
CAMPA, A ;
GIANSANTI, A ;
TENENBAUM, A ;
LEVI, D ;
RAGNISCO, O .
PHYSICAL REVIEW B, 1993, 48 (14) :10168-10182
[4]   ON THE INFINITE-DIMENSIONAL SYMMETRY GROUP OF THE DAVEY-STEWARTSON EQUATIONS [J].
CHAMPAGNE, B ;
WINTERNITZ, P .
JOURNAL OF MATHEMATICAL PHYSICS, 1988, 29 (01) :1-8
[5]   SYMMETRY REDUCTION FOR THE KADOMTSEV-PETVIASHVILI EQUATION USING A LOOP ALGEBRA [J].
DAVID, D ;
KAMRAN, N ;
LEVI, D ;
WINTERNITZ, P .
JOURNAL OF MATHEMATICAL PHYSICS, 1986, 27 (05) :1225-1237
[6]   SUBALGEBRAS OF LOOP ALGEBRAS AND SYMMETRIES OF THE KADOMTSEV-PETVIASHVILI EQUATION [J].
DAVID, D ;
KAMRAN, N ;
LEVI, D ;
WINTERNITZ, P .
PHYSICAL REVIEW LETTERS, 1985, 55 (20) :2111-2113
[7]   SYMMETRIES OF VARIABLE-COEFFICIENT KORTEWEG-DEVRIES EQUATIONS [J].
GAZEAU, JP ;
WINTERNITZ, P .
JOURNAL OF MATHEMATICAL PHYSICS, 1992, 33 (12) :4087-4102
[8]  
GAZEAU JP, 1992, PHYS LETT A, V167, P246
[9]  
GUNGOR F, IN PRESS CAN J PHYS
[10]  
Jacobson N., 1979, Lie algebras
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