Geodesic
Integrable lattices
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 2, pp. 217-228

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We propose a method for constructing integrable lattices starting from dynamic systems with two different parameterizations of the canonical variables and hence two independent Bäcklund flows. We construct integrable lattices corresponding to generalizations of the nonlinear Schrödinger equation. We discuss the Toda, Volterra, and Heisenberg models in detail. For these systems, as well as for the Landau–Lifshitz model, we obtain totally discrete Lagrangians. We also discuss the relation of these systems to the Hirota equations. 
@article{TMF_1999_118_2_a3,
     author = {V. G. Marikhin and A. B. Shabat},
     title = {Integrable lattices},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {217--228},
     publisher = {mathdoc},
     volume = {118},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_2_a3/}
}
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V. G. Marikhin; A. B. Shabat. Integrable lattices. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 2, pp. 217-228. http://geodesic.mathdoc.fr/item/TMF_1999_118_2_a3/