Geodesic
Symmetries of the Discrete Nonlinear Schr\"odinger Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 3, pp. 379-387

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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. 
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     author = {R. Hernandez Heredero and D. Levi and P. Winternitz},
     title = {Symmetries of the {Discrete} {Nonlinear} {Schr\"odinger} {Equation}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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R. Hernandez Heredero; D. Levi; P. Winternitz. Symmetries of the Discrete Nonlinear Schr\"odinger Equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 3, pp. 379-387. http://geodesic.mathdoc.fr/item/TMF_2001_127_3_a3/