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.

Levi, D., Rodriguez, M.a. (1992). SYMMETRY GROUP OF PARTIAL-DIFFERENTIAL EQUATIONS AND OF DIFFERENTIAL DIFFERENCE-EQUATIONS - THE TODA LATTICE VERSUS THE KORTEWEG-DEVRIES EQUATION. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 25(15), L975-L979 [10.1088/0305-4470/25/15/013].

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

LEVI, Decio;
1992-01-01

Abstract

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.
1992
Levi, D., Rodriguez, M.a. (1992). SYMMETRY GROUP OF PARTIAL-DIFFERENTIAL EQUATIONS AND OF DIFFERENTIAL DIFFERENCE-EQUATIONS - THE TODA LATTICE VERSUS THE KORTEWEG-DEVRIES EQUATION. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 25(15), L975-L979 [10.1088/0305-4470/25/15/013].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/136955
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