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Three-dimensional lattice of Bäcklund transformations of integrable cases of the Davey–Stewartson system

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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.

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, RAS, Chernogolovka, Russia

    V. G. Marikhin

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  1. V. G. Marikhin
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Correspondence to V. G. Marikhin.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 189, No. 3, pp. 362–370, December, 2016.

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Marikhin, V.G. Three-dimensional lattice of Bäcklund transformations of integrable cases of the Davey–Stewartson system. Theor Math Phys 189, 1718–1725 (2016). https://doi.org/10.1134/S0040577916120047

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  • DOI: https://doi.org/10.1134/S0040577916120047

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