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

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

DOI: 10.4213/tmf9213

 English version: Theoretical and Mathematical Physics, 2016, 189:3, 1718–1725

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