Ferapontov_discrete1.pdf (1.06 MB)
Download file

On the classification of discrete Hirota-type equations in 3D

Download (1.06 MB)
journal contribution
posted on 05.02.2016, 11:02 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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

International Mathematics Research Notices

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.

Publisher

© The Authors. Published by Oxford University Press.

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2014

Notes

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

ISSN

1687-3017

Language

en