1,721,055 research outputs found
THE CYLINDRICAL KADOMTSEV-PETVIASHVILI EQUATION - ITS KAC-MOODY-VIRASORO ALGEBRA AND RELATION TO KP EQUATION
No full textContinuous symmetries of difference equations
No full textLie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict them to point symmetries, but to allow them to also transform the lattice
CONTINUOUS SYMMETRIES OF DISCRETE EQUATIONS
No full textLie group techniques for solving differential equations are extended to differential-difference equations. As an application, it is shown that the two-dimensional Toda lattice has an infinite dimensional symmetry group with a Kac-Moody-Virasoro Lie algebra
Lie point symmetries and commuting flows for equations on lattices
No full textDifferent symmetry formalisms for difference equations on lattices are reviewed and applied to perform symmetry reduction for both linear and nonlinear partial difference equations. Both Lie point symmetries and generalized symmetries are considered and applied to the discrete heat equation and to the integrable discrete time Toda lattice
Lie point symmetries of difference equations and lattices RID G-3580-2010
No full textA method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to several examples. The found symmetry groups are used to obtain particular solutions of differential-difference equations
Continuous symmetries of equations on lattices RID G-3580-2010
No full textA method is presented for calculating the Lie point. symmetries of difference equations with one, or several, independent variables. The equations are given on a priori specified lattices. The Lie transformations act on the lattice, as well as on the equation. The transformations take solutions into solutions and can be used to perform symmetry reduction
Symmetries of discrete dynamical systems
No full textDifferential-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
- …
