I. T. Habibullin, M. N. Kuznetsova, “A classification algorithm for integrable two-dimensional lattices via Lie–Rinehart algebras”, TMF, 203:1 (2020), 161–173; Theoret. and Math. Phys., 203:1 (2020), 569

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 203, Number 1, Pages 161–173
DOI: https://doi.org/10.4213/tmf9786 (Mi tmf9786)

This article is cited in 16 scientific papers (total in 16 papers)

A classification algorithm for integrable two-dimensional lattices via Lie–Rinehart algebras

I. T. Habibullin^ab, M. N. Kuznetsova^a

^a Institute of Mathematics with Computing Centre — Subdivision of the Ufa Federal Research Centre of the~Russian Academy of Science, Ufa, Russia
^b Bashkir State University, Ufa, Russia

Full-text PDF (510 kB) Citations (16)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf9786

Abstract: We study the problem of the integrable classification of nonlinear lattices depending on one discrete and two continuous variables. By integrability, we mean the presence of reductions of a chain to a system of hyperbolic equations of an arbitrarily high order that are integrable in the Darboux sense. Darboux integrability admits a remarkable algebraic interpretation: the Lie–Rinehart algebras related to both characteristic directions corresponding to the reduced system of hyperbolic equations must have a finite dimension. We discuss a classification algorithm based on the properties of the characteristic algebra and present some classification results. We find new examples of integrable equations.

Keywords: two-dimensional integrable lattice, $x$-integral, integrable reduction, cutoff condition, open lattice, Darboux-integrable system, characteristic Lie algebra.

Received: 29.07.2019
Revised: 22.10.2019

English version:
Theoretical and Mathematical Physics, 2020, Volume 203, Issue 1, Pages 569–581
DOI: https://doi.org/10.1134/S0040577920040121

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: I. T. Habibullin, M. N. Kuznetsova, “A classification algorithm for integrable two-dimensional lattices via Lie–Rinehart algebras”, TMF, 203:1 (2020), 161–173; Theoret. and Math. Phys., 203:1 (2020), 569–581

Citation in format AMSBIB

\Bibitem{HabKuz20}

\by I.~T.~Habibullin, M.~N.~Kuznetsova

\paper A~classification algorithm for integrable two-dimensional lattices

via Lie--Rinehart algebras

\jour TMF

\yr 2020

\vol 203

\issue 1

\pages 161--173

\mathnet{http://mi.mathnet.ru/tmf9786}

\crossref{https://doi.org/10.4213/tmf9786}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4082005}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2020TMP...203..569H}

\elib{https://elibrary.ru/item.asp?id=43279185}

\transl

\jour Theoret. and Math. Phys.

\yr 2020

\vol 203

\issue 1

\pages 569--581

\crossref{https://doi.org/10.1134/S0040577920040121}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000529685500012}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85084123541}

Linking options:

https://www.mathnet.ru/eng/tmf9786

https://doi.org/10.4213/tmf9786

https://www.mathnet.ru/eng/tmf/v203/i1/p161

This publication is cited in the following 16 articles:

I.T. Habibullin, A.U. Sakieva, “On integrable reductions of two-dimensional Toda-type lattices”, Partial Differential Equations in Applied Mathematics, 11 (2024), 100854
A. R. Khakimova, “Darboux-integrable Reductions of the Hirota–Miwa Type Discrete Equations”, Lobachevskii J Math, 45:6 (2024), 2717
Ismagil T. Habibullin, Aigul R. Khakimova, “Higher Symmetries of Lattices in 3D”, Regul. Chaotic Dyn., 29:6 (2024), 853–865
Ufa Math. J., 16:4 (2024), 124–135
M. N. Kuznetsova, I. T. Habibullin, A. R. Khakimova, “On the problem of classifying integrable chains with three independent variables”, Theoret. and Math. Phys., 215:2 (2023), 667–690
M. N. Kuznetsova, “Construction of localized particular solutions of chains with three independent variables”, Theoret. and Math. Phys., 216:2 (2023), 1158–1167
I. T. Habibullin, A. R. Khakimova, “On the classification of nonlinear integrable three-dimensional chains via characteristic Lie algebras”, Theoret. and Math. Phys., 217:1 (2023), 1541–1573
S. V. Smirnov, “Integral preserving discretization of 2D Toda lattices”, J. Phys. A: Math. Theor., 56:26 (2023), 265204
I. T. Habibullin, A. R. Khakimova, “Integrals and characteristic algebras for systems of discrete equations on a quadrilateral graph”, Theoret. and Math. Phys., 213:2 (2022), 1589–1612
I. T. Habibullin, A. R. Khakimova, “Algebraic reductions of discrete equations of Hirota-Miwa type”, Ufa Math. J., 14:4 (2022), 113–126
D. V. Millionshchikov, S. V. Smirnov, “Characteristic algebras and integrable exponential systems”, Ufa Math. J., 13:2 (2021), 41–69
Maria N. Kuznetsova, “Lax Pair for a Novel Two-Dimensional Lattice”, SIGMA, 17 (2021), 088, 13 pp.
I. T. Habibullin, M. N. Kuznetsova, “An algebraic criterion of the Darboux integrability of differential-difference equations and systems”, J. Phys. A-Math. Theor., 54:50 (2021), 505201
I. T. Habibullin, A. R. Khakimova, “Characteristic Lie algebras of integrable differential-difference equations in 3D”, J. Phys. A-Math. Theor., 54:29 (2021), 295202
Habibullin I.T. Kuznetsova M.N. Sakieva A.U., “Integrability Conditions For Two-Dimensional Toda-Like Equations”, J. Phys. A-Math. Theor., 53:39 (2020), 395203
Ferapontov E.V. Habibullin I.T. Kuznetsova M.N. Novikov V.S., “On a Class of 2D Integrable Lattice Equations”, J. Math. Phys., 61:7 (2020), 073505

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

Statistics & downloads:
Abstract page:	480
Full-text PDF :	101
References:	85
First page:	10

Registration to the website

Logotypes