R. N. Garifullin, A. V. Mikhailov, R. I. Yamilov, “Discrete equation on a square lattice with a nonstandard structure of generalized symmetries”, TMF, 180:1 (2014), 17–34; Theoret. and Math. Phys., 180:1 (2014), 765

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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 180, Number 1, Pages 17–34
DOI: https://doi.org/10.4213/tmf8663 (Mi tmf8663)

This article is cited in 20 scientific papers (total in 20 papers)

Discrete equation on a square lattice with a nonstandard structure of generalized symmetries

R. N. Garifullin^a, A. V. Mikhailov^b, R. I. Yamilov^a

^a Institute of Mathematics with Computing Center, Ufa Science Center, RAS, Ufa, Russia
^b University of Leeds, Department of Applied Mathematics, Leeds, UK

Full-text PDF (489 kB) Citations (20)

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DOI: https://doi.org/10.4213/tmf8663

Abstract: We clarify the integrability nature of a recently found discrete equation on the square lattice with a nonstandard symmetry structure. We find its $L$–$A$ pair and show that it is also nonstandard. For this discrete equation, we construct the hierarchies of both generalized symmetries and conservation laws. This equation yields two integrable systems of hyperbolic type. The hierarchies of generalized symmetries and conservation laws are also nonstandard compared with known equations in this class.

Keywords: discrete integrable equation, generalized symmetry, conservation law, $L$–$A$ pair.

Received: 18.02.2014

English version:
Theoretical and Mathematical Physics, 2014, Volume 180, Issue 1, Pages 765–780
DOI: https://doi.org/10.1007/s11232-014-0178-6

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: R. N. Garifullin, A. V. Mikhailov, R. I. Yamilov, “Discrete equation on a square lattice with a nonstandard structure of generalized symmetries”, TMF, 180:1 (2014), 17–34; Theoret. and Math. Phys., 180:1 (2014), 765–780

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This publication is cited in the following 20 articles:

Vladimir Novikov, Jing Ping Wang, “Integrability of Nonabelian Differential–Difference Equations: The Symmetry Approach”, Commun. Math. Phys., 406:1 (2025)
V. E. Adler, “3D consistency of negative flows”, Theoret. and Math. Phys., 221:2 (2024), 1836–1851
R. N. Garifullin, “Classification of semidiscrete equations of hyperbolic type. The case of third-order symmetries”, Theoret. and Math. Phys., 217:2 (2023), 1767–1776
Adler V.E., “Painleve Type Reductions For the Non-Abelian Volterra Lattices”, J. Phys. A-Math. Theor., 54:3 (2021), 035204
G. Gubbiotti, “Algebraic entropy of a class of five-point differential-difference equations”, Symmetry-Basel, 11:3 (2019), 432
R. N. Garifullin, G. Gubbiotti, R. I. Yamilov, “Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations”, J. Nonlinear Math. Phys., 26:3 (2019), 333–357
R. N. Garifullin, R. I. Yamilov, “An unusual series of autonomous discrete integrable equations on a square lattice”, Theoret. and Math. Phys., 200:1 (2019), 966–984
R. N. Garifullin, R. I. Yamilov, D. Levi, “Classification of five-point differential-difference equations II”, J. Phys. A-Math. Theor., 51:6 (2018), 065204
V. E. Adler, “Integrable seven-point discrete equations and second-order evolution chains”, Theoret. and Math. Phys., 195:1 (2018), 513–528
I. T. Habibullin, A. R. Khakimova, “On the recursion operators for integrable equations”, J. Phys. A-Math. Theor., 51:42 (2018), 425202
P. Xenitidis, “Determining the symmetries of difference equations”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 474:2219 (2018), 20180340
R. N. Garifullin, R. I. Yamilov, “On the Integrability of a Lattice Equation with Two Continuum Limits”, J. Math. Sci. (N. Y.), 252:2 (2021), 283–289
Pavlos Xenitidis, “Deautonomizations of integrable equations and their reductions”, Journal of Integrable Systems, 3:1 (2018)
R. N. Garifullin, R. I. Yamilov, D. Levi, “Classification of five-point differential-difference equations”, J. Phys. A-Math. Theor., 50:12 (2017), 125201
Ufa Math. J., 9:3 (2017), 158–164
G. Gubbiotti, C. Scimiterna, D. Levi, “The non-autonomous YdKN equation and generalized symmetries of Boll equations”, J. Math. Phys., 58:5 (2017), 053507
V. E. Adler, “Integrable Möbius-invariant evolutionary lattices of second order”, Funct. Anal. Appl., 50:4 (2016), 257–267
A. V. Mikhailov, “Formal diagonalisation of Lax–Darboux schemes”, Model. i analiz inform. sistem, 22:6 (2015), 795–817
R N Garifullin, I T Habibullin, R I Yamilov, “Peculiar symmetry structure of some known discrete nonautonomous equations”, J. Phys. A: Math. Theor., 48:23 (2015), 235201
V. E. Adler, “Necessary integrability conditions for evolutionary lattice equations”, Theoret. and Math. Phys., 181:2 (2014), 1367–1382

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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