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Title: On the classification of discrete Hirota-type equations in 3D
Authors: Ferapontov, E.V.
Novikov, V.S.
Roustemoglou, Ilia
Keywords: Discrete integrable systems in 3D
Dispersionless limit
Hydrodynamic reductions
Hirota-type equations
Issue Date: 2014
Publisher: © The Authors. Published by Oxford University Press.
Citation: FERAPONTOV, E.V., NOVIKOV, V.S. and ROUSTEMOGLOU, I., 2014. On the classification of discrete Hirota-type equations in 3D. International Mathematics Research Notices, (13), pp. 4933-4974.
Abstract: In the series of recent publications [15, 16, 18, 21] we have proposed a novel approach to the classification of integrable differential/difference equations in 3D based on the requirement that hydrodynamic reductions of the corresponding dispersionless limits are `inherited' by the dispersive equations. In this paper we extend this to the fully discrete case. Based on the method of deformations of hydrodynamic reductions, we classify 3D discrete integrable Hirota-type equations within various particularly interesting subclasses. Our method can be viewed as an alternative to the conventional multi-dimensional consistency approach.
Description: This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record FERAPONTOV, E.V., NOVIKOV, V.S. and ROUSTEMOGLOU, I., 2014. On the classification of discrete Hirota-type equations in 3D. International Mathematics Research Notices, (13), pp. 4933-4974. is available online at: http://dx.doi.org/10.1093/imrn/rnu086
Version: Accepted for publication
DOI: 10.1093/imrn/rnu086
URI: https://dspace.lboro.ac.uk/2134/20230
Publisher Link: http://dx.doi.org/10.1093/imrn/rnu086
ISSN: 1687-3017
Appears in Collections:Published Articles (Maths)

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