Geodesic
Three-dimensional lattice of B\"acklund transformations of integrable cases of the~Davey--Stewartson system
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 3, pp. 362-370

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We construct a three-dimensional octahedral lattice of Bäcklund transformations of integrable cases of the Davey–Stewartson system. At the lattice sites, we arrange functions, which, on one hand, are used to define the dynamical variables of the Davey–Stewartson system and, on the other hand, are connected by bilinear relations of the Hirota type. One of the lattice equations is a purely discrete six-point equation that coincides with the famous Hirota equation.
Keywords: Bäcklund transformation, Davey–Stewartson system
Mots-clés : Hirota equation. 
@article{TMF_2016_189_3_a3,
     author = {V. G. Marikhin},
     title = {Three-dimensional lattice of {B\"acklund} transformations of integrable cases of {the~Davey--Stewartson} system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {362--370},
     publisher = {mathdoc},
     volume = {189},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_189_3_a3/}
}
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V. G. Marikhin. Three-dimensional lattice of B\"acklund transformations of integrable cases of the~Davey--Stewartson system. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 3, pp. 362-370. http://geodesic.mathdoc.fr/item/TMF_2016_189_3_a3/