This article is cited in 8 papers

Symmetries of the Discrete Nonlinear Schrödinger Equation

R. Hernandez Heredero^a, D. Levi^b, P. Winternitz<sup>c

a</sup> Universidad Complutense, Departamento de Fisica Teorica II
^b INFN — National Institute of Nuclear Physics
^c Université de Montréal

Abstract: The Lie algebra $L(h)$ of point symmetries of a discrete analogue of the nonlinear Schrödinger equation (NLS) is described. In the continuous limit, the discrete equation is transformed into the NLS, while the structure of the Lie algebra changes: a contraction occurs with the lattice spacing $h$ as the contraction parameter. A five-dimensional subspace of $L(h)$, generated by both point and generalized symmetries, transforms into the five-dimensional point symmetry algebra of the NLS.

DOI: 10.4213/tmf465

 English version: Theoretical and Mathematical Physics, 2001, 127:3, 729–737

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