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

This article is cited in 12 scientific papers (total in 12 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

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

Full text: PDF file (489 kB)
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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
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    Citing articles on Google Scholar: Russian citations, English citations
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    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. Gubbiotti G., “Algebraic Entropy of a Class of Five-Point Differential-Difference Equations”, Symmetry-Basel, 11:3 (2019), 432  crossref  isi
    12. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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