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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 3, Pages 362–370
DOI: https://doi.org/10.4213/tmf9213 (Mi tmf9213) 		 
Three-dimensional lattice of Bäcklund transformations of integrable cases of the Davey–Stewartson system

V. G. Marikhin

Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow region, Russia
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DOI: https://doi.org/10.4213/tmf9213
Abstract: 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, Hirota equation.
Received: 21.04.2016
Revised: 15.05.2016
English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 3, Pages 1718–1725
DOI: https://doi.org/10.1134/S0040577916120047
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. G. Marikhin, “Three-dimensional lattice of Bäcklund transformations of integrable cases of the Davey–Stewartson system”, TMF, 189:3 (2016), 362–370; Theoret. and Math. Phys., 189:3 (2016), 1718–1725
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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