SYMMETRY GROUP OF PARTIAL-DIFFERENTIAL EQUATIONS AND OF DIFFERENTIAL DIFFERENCE-EQUATIONS - THE TODA LATTICE VERSUS THE KORTEWEG-DEVRIES EQUATION

In this work we correlate the symmetry group of the continuous transformations of the Toda lattice to that of the Korteweg-de Vries equation. We show how, by taking into account the continuous limit of the Toda, the four-parameter symmetry group of the Toda is contained in that of the KdV equation. By an inverse process, discretization of the symmetry group of the KdV, we find a discrete clement of the symmetry group of the Toda lattice, which gives, by symmetry reduction, its soliton solution.