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On a class of 2D integrable lattice equations

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journal contribution
posted on 25.06.2020 by Evgeny Ferapontov, Ismagil Habibullin, Mariya Kuznetsova, Vladimir Novikov
We develop a new approach to the classification of integrable equations of the form uxy = f(u, ux, uy, Δzu Δu, Δ zz¯u) where Δz and Δz¯ are the forward/backward discrete derivatives. The following 2-step classification procedure is proposed: (1) First we require that the dispersionless limit of the equation is integrable, that is, its characteristic variety defines a conformal structure which is Einstein-Weyl on every solution. (2) Secondly, to the candidate equations selected at the previous step we apply the test of Darboux integrability of reductions obtained by imposing suitable cut-off conditions

Funding

Challenges of dispersionless integrability: Hirota type equations

Engineering and Physical Sciences Research Council

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History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Mathematical Physics

Volume

61

Issue

7

Publisher

AIP Publishing

Version

AM (Accepted Manuscript)

Rights holder

© The Authors

Publisher statement

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Journal of Mathematical Physics, 61 (7), 073505 and may be found at https://aip.scitation.org/doi/abs/10.1063/5.0013697.

Acceptance date

23/06/2020

Publication date

2020-07-13

Copyright date

2020

ISSN

0022-2488

eISSN

1089-7658

Language

en

Depositor

Prof Evgeny Ferapontov . Deposit date: 24 June 2020

Article number

073505

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