On the classification of discrete Hirota-type equations in 3D
journal contributionposted on 2016-02-05, 11:02 authored by Evgeny FerapontovEvgeny Ferapontov, Vladimir NovikovVladimir Novikov, Ilia Roustemoglou
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.
- Mathematical Sciences
Published inInternational Mathematics Research Notices
CitationFERAPONTOV, 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.
Publisher© The Authors. Published by Oxford University Press.
- AM (Accepted Manuscript)
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NotesThis 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