Two different methods of finding Lie point symmetries of differential-difference equations are presented and applied to the two-dimensional Toda lattice. Continuous symmetries are combined with discrete ones to obtain various reductions to lower dimensional equations, in particular, to differential equations of the delay type. The concept of conditional symmetries is extended from purely differential to differential-difference equations and shown to incorporate Backlund transformations.
Levi, D., Winternitz, P. (1993). SYMMETRIES AND CONDITIONAL SYMMETRIES OF DIFFERENTIAL-DIFFERENCE EQUATIONS. JOURNAL OF MATHEMATICAL PHYSICS, 34(8), 3713-3730 [10.1063/1.530054].
SYMMETRIES AND CONDITIONAL SYMMETRIES OF DIFFERENTIAL-DIFFERENCE EQUATIONS
LEVI, Decio;
1993-01-01
Abstract
Two different methods of finding Lie point symmetries of differential-difference equations are presented and applied to the two-dimensional Toda lattice. Continuous symmetries are combined with discrete ones to obtain various reductions to lower dimensional equations, in particular, to differential equations of the delay type. The concept of conditional symmetries is extended from purely differential to differential-difference equations and shown to incorporate Backlund transformations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
