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.
1993
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/154653
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