Geodesic
General solutions of the two-dimensional system of Volterra equations which realize the B\"acklund transformation for the Toda lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 2, pp. 216-224

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It is shown that a two-dimensional system of Volterra equations (or difference Kortewegde Vries equations) is a Bäcklund transformation for the Toda lattice in two-dimensional space. This makes it possible to find the explicit form of the general selutions of these equations, which depend on the required number of arbitrary functions, on the basis of the known general solutions for the Toda lattice [1]. At the same time, the solutions of one-dimensional Volterra equations (and aIso numerous related nonlinear differentialdifference equations) are obtained as special cases of the general solutions. 
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     author = {A. N. Leznov and M. V. Saveliev and V. G. Smirnov},
     title = {General solutions of the two-dimensional system of {Volterra} equations which realize the {B\"acklund} transformation for the {Toda} lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {47},
     number = {2},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_47_2_a6/}
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A. N. Leznov; M. V. Saveliev; V. G. Smirnov. General solutions of the two-dimensional system of Volterra equations which realize the B\"acklund transformation for the Toda lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 2, pp. 216-224. http://geodesic.mathdoc.fr/item/TMF_1981_47_2_a6/