Symmetry group of partial differential equations and of differential difference equations: the Toda lattice versus the Korteweg-de Vries equation
- 7 August 1992
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 25 (15) , L975-L979
- https://doi.org/10.1088/0305-4470/25/15/013
Abstract
The authors correlate the symmetry group of the continuous transformations of the Toda lattice to that of the Korteweg-de Vries equation. They show how, by taking into account the continuous limit of the Toda lattice the four-parameter symmetry group of the Toda lattice is contained in that of the KdV equation. By an inverse process, discretization of the symmetry group of the KdV equation, they find a discrete element of the symmetry group of the Toda lattice, which gives, by symmetry reduction, its soliton solution.Keywords
This publication has 2 references indexed in Scilit:
- Continuous symmetries of discrete equationsPhysics Letters A, 1991
- Canonically Conjugate Variables for the Korteweg-de Vries Equation and the Toda Lattice with Periodic Boundary ConditionsProgress of Theoretical Physics, 1976