V. E. Adler, “Necessary integrability conditions for evolutionary lattice equations”, TMF, 181:2 (2014), 276–295; Theoret. and Math. Phys., 181:2 (2014), 1367

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, 2014, Volume 181, Number 2, Pages 276–295
DOI: https://doi.org/10.4213/tmf8722 (Mi tmf8722)

This article is cited in 10 scientific papers (total in 10 papers)

Necessary integrability conditions for evolutionary lattice equations

V. E. Adler

Landau Institute for Theoretical Physics, RAS, Chernogolovka, Russia

Full-text PDF (496 kB) Citations (10)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf8722

Abstract: We study the structure of solutions of the Lax equation

D_{t} (G) = [F, G]

$D_t(G)=[F,G]$ for formal series in powers of the shift operator. We show that if an equation with a given series

F

$F$ of degree

m

$m$ admits a solution

G

$G$ of degree

k

$k$ , then it also admits a solution

H

$H$ of degree

m

$m$ such that

H^{k} = G^{m}

$H^k=G^m$ . We use this property to derive necessary integrability conditions for scalar evolutionary lattices.

Keywords: Volterra-type lattice, higher symmetry, conservation law, integrability test.

Received: 01.06.2014

English version:
Theoretical and Mathematical Physics, 2014, Volume 181, Issue 2, Pages 1367–1382
DOI: https://doi.org/10.1007/s11232-014-0218-2

Bibliographic databases:

PACS: 02.30.Ik

MSC: 37K10

Language: Russian

Citation: V. E. Adler, “Necessary integrability conditions for evolutionary lattice equations”, TMF, 181:2 (2014), 276–295; Theoret. and Math. Phys., 181:2 (2014), 1367–1382

Citation in format AMSBIB

\Bibitem{Adl14}

\by V.~E.~Adler

\paper Necessary integrability conditions for evolutionary lattice

equations

\jour TMF

\yr 2014

\vol 181

\issue 2

\pages 276--295

\mathnet{http://mi.mathnet.ru/tmf8722}

\crossref{https://doi.org/10.4213/tmf8722}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3344450}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2014TMP...181.1367A}

\elib{https://elibrary.ru/item.asp?id=22834543}

\transl

\jour Theoret. and Math. Phys.

\yr 2014

\vol 181

\issue 2

\pages 1367--1382

\crossref{https://doi.org/10.1007/s11232-014-0218-2}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000345836900003}

\elib{https://elibrary.ru/item.asp?id=24012381}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84915746229}

Linking options:

https://www.mathnet.ru/eng/tmf8722

https://doi.org/10.4213/tmf8722

https://www.mathnet.ru/eng/tmf/v181/i2/p276

This publication is cited in the following 10 articles:

Vladimir Novikov, Jing Ping Wang, “Integrability of Nonabelian Differential–Difference Equations: The Symmetry Approach”, Commun. Math. Phys., 406:1 (2025)
Alexander V. Mikhailov, Vladimir S. Novikov, Jing Ping Wang, “Perturbative Symmetry Approach for Differential–Difference Equations”, Commun. Math. Phys., 393:2 (2022), 1063
Rustem N. Garifullin, Ravil I. Yamilov, “Integrable Modifications of the Ito–Narita–Bogoyavlensky Equation”, SIGMA, 15 (2019), 062, 15 pp.
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
R. N. Garifullin, R. I. Yamilov, D. Levi, “Classification of five-point differential-difference equations”, J. Phys. A-Math. Theor., 50:12 (2017), 125201
V. E. Adler, “Integrability test for evolutionary lattice equations of higher order”, J. Symbolic Comput., 74 (2016), 125–139
S. V. Dmitriev, E. A. Korznikova, Yu. A. Baimova, M. G. Velarde, “Discrete breathers in crystals”, Phys. Usp., 59:5 (2016), 446–461
V. E. Adler, “Integrable Möbius-invariant evolutionary lattices of second order”, Funct. Anal. Appl., 50:4 (2016), 257–267
R. N. Garifullin, R. I. Yamilov, D. Levi, “Non-invertible transformations of differential-difference equations”, J. Phys. A-Math. Theor., 49:37 (2016), 37LT01

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

Statistics & downloads:
Abstract page:	519
Full-text PDF :	199
References:	76
First page:	27

Registration to the website

Logotypes