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Funktsional. Anal. i Prilozhen., 2016, Volume 50, Issue 4, Pages 13–25 (Mi faa3255)  

This article is cited in 5 scientific papers (total in 5 papers)

Integrable Möbius-invariant evolutionary lattices of second order

V. E. Adler

L.D. Landau Institute for Theoretical Physics, Chernogolovka, Russia

Abstract: We solve the classification problem for integrable lattices of the form $u_{,t}=f(u_{-2},…,u_2)$ under the additional assumption of invariance with respect to the group of linear-fractional transformations. The obtained list contains five equations, including three new ones. Difference Miura-type substitutions are found, which relate these equations to known polynomial lattices. We also present some classification results for generic lattices.

Keywords: integrability, symmetry, conservation law, Möbius invariantm cross-ratio.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00289a
This work was supported by RFBR grant No. 16-01-00289a.


DOI: https://doi.org/10.4213/faa3255

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English version:
Functional Analysis and Its Applications, 2016, 50:4, 257–267

Bibliographic databases:

UDC: 517.929+517.957+517.958+517.962.24
Received: 04.05.2016

Citation: V. E. Adler, “Integrable Möbius-invariant evolutionary lattices of second order”, Funktsional. Anal. i Prilozhen., 50:4 (2016), 13–25; Funct. Anal. Appl., 50:4 (2016), 257–267

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. R. N. Garifullin, R. I. Yamilov, D. Levi, “Classification of five-point differential-difference equations”, J. Phys. A, 50:12 (2017), 125201, 27 pp.  crossref  mathscinet  zmath  isi  scopus
    2. Ufa Math. J., 9:3 (2017), 158–164  mathnet  crossref  mathscinet  isi  elib  elib  scopus
    3. R. N. Garifullin, R. I. Yamilov, D. Levi, “Classification of five-point differential-difference equations II”, J. Phys. A, 51:6 (2018), 065204, 16 pp.  crossref  mathscinet  zmath  isi  scopus
    4. 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
    5. Gubbiotti G., “Algebraic Entropy of a Class of Five-Point Differential-Difference Equations”, Symmetry-Basel, 11:3 (2019), 432  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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