RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
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


TMF, 2014, Volume 181, Number 2, Pages 276–295 (Mi tmf8722)  

This article is cited in 7 scientific papers (total in 7 papers)

Necessary integrability conditions for evolutionary lattice equations

V. E. Adler

Landau Institute for Theoretical Physics, RAS, Chernogolovka, Russia

Abstract: We study the structure of solutions of the Lax equation $D_t(G)=[F,G]$ for formal series in powers of the shift operator. We show that if an equation with a given series $F$ of degree $m$ admits a solution $G$ of degree $k$, then it also admits a solution $H$ of degree $m$ such that $H^k=G^m$. We use this property to derive necessary integrability conditions for scalar evolutionary lattices.

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

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

Full text: PDF file (496 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2014, 181:2, 1367–1382

Bibliographic databases:

PACS: 02.30.Ik
MSC: 37K10
Received: 01.06.2014

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://www.ams.org/mathscinet-getitem?mr=3344450}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2014TMP...181.1367A}
\elib{http://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{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000345836900003}
\elib{http://elibrary.ru/item.asp?id=24012381}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84915746229}


Linking options:
  • http://mi.mathnet.ru/eng/tmf8722
  • https://doi.org/10.4213/tmf8722
  • http://mi.mathnet.ru/eng/tmf/v181/i2/p276

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. V. E. Adler, “Integrability test for evolutionary lattice equations of higher order”, J. Symbolic Comput., 74 (2016), 125–139  crossref  mathscinet  zmath  isi  elib  scopus
    2. S. V. Dmitriev, E. A. Korznikova, Yu. A. Baimova, M. G. Velarde, “Discrete breathers in crystals”, Phys. Usp., 59:5 (2016), 446–461  mathnet  crossref  crossref  adsnasa  isi  elib
    3. V. E. Adler, “Integrable Möbius-invariant evolutionary lattices of second order”, Funct. Anal. Appl., 50:4 (2016), 257–267  mathnet  crossref  crossref  mathscinet  isi  elib
    4. R. N. Garifullin, R. I. Yamilov, D. Levi, “Non-invertible transformations of differential-difference equations”, J. Phys. A-Math. Theor., 49:37 (2016), 37LT01  crossref  mathscinet  zmath  isi  elib  scopus
    5. R. N. Garifullin, R. I. Yamilov, D. Levi, “Classification of five-point differential-difference equations”, J. Phys. A-Math. Theor., 50:12 (2017), 125201  crossref  mathscinet  zmath  isi  scopus
    6. 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  crossref  mathscinet  zmath  isi  scopus
    7. V. E. Adler, “Integrable seven-point discrete equations and second-order evolution chains”, Theoret. and Math. Phys., 195:1 (2018), 513–528  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:217
    Full text:33
    References:30
    First page:27

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019