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

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS


Personal entry:
Save password
Forgotten password?

TMF, 2014, Volume 180, Number 1, Pages 17–34 (Mi tmf8663)  

This article is cited in 14 scientific papers (total in 14 papers)

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

R. N. Garifullina, A. V. Mikhailovb, R. I. Yamilova

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

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


Full text: PDF file (489 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2014, 180:1, 765–780

Bibliographic databases:

Received: 18.02.2014

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

Citation in format AMSBIB
\by R.~N.~Garifullin, A.~V.~Mikhailov, R.~I.~Yamilov
\paper Discrete equation on a~square lattice with a~nonstandard structure of generalized symmetries
\jour TMF
\yr 2014
\vol 180
\issue 1
\pages 17--34
\jour Theoret. and Math. Phys.
\yr 2014
\vol 180
\issue 1
\pages 765--780

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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, “Necessary integrability conditions for evolutionary lattice equations”, Theoret. and Math. Phys., 181:2 (2014), 1367–1382  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. A. V. Mikhailov, “Formal diagonalisation of Lax–Darboux schemes”, Model. i analiz inform. sistem, 22:6 (2015), 795–817  mathnet  crossref  mathscinet  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, “Classification of five-point differential-difference equations”, J. Phys. A-Math. Theor., 50:12 (2017), 125201  crossref  mathscinet  zmath  isi  scopus
    5. Ufa Math. J., 9:3 (2017), 158–164  mathnet  crossref  mathscinet  isi  elib  elib
    6. G. Gubbiotti, C. Scimiterna, D. Levi, “The non-autonomous YdKN equation and generalized symmetries of Boll equations”, J. Math. Phys., 58:5 (2017), 053507  crossref  mathscinet  zmath  isi  scopus
    7. 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
    8. 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
    9. I. T. Habibullin, A. R. Khakimova, “On the recursion operators for integrable equations”, J. Phys. A-Math. Theor., 51:42 (2018), 425202  crossref  isi  scopus
    10. P. Xenitidis, “Determining the symmetries of difference equations”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 474:2219 (2018), 20180340  crossref  mathscinet  isi  scopus
    11. R. N. Garifullin, R. I. Yamilov, “Ob integriruemosti reshetochnykh uravnenii s dvumya kontinualnymi predelami”, Matematicheskaya fizika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 152, VINITI RAN, M., 2018, 159–164  mathnet  mathscinet
    12. Gubbiotti G., “Algebraic Entropy of a Class of Five-Point Differential-Difference Equations”, Symmetry-Basel, 11:3 (2019), 432  crossref  isi
    13. Garifullin R.N. Gubbiotti G. Yamilov I R., “Integrable Discrete Autonomous Quad-Equations Admitting, as Generalized Symmetries, Known Five-Point Differential-Difference Equations”, J. Nonlinear Math. Phys., 26:3 (2019), 333–357  crossref  isi
    14. 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  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:350
    Full text:118
    First page:125

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021