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TMF, 2015, Volume 182, Number 2, Pages 231–255 (Mi tmf8772)  

This article is cited in 6 scientific papers (total in 6 papers)

Darboux integrability of discrete two-dimensional Toda lattices

S. V. Smirnov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We prove the Darboux integrability of semidiscrete and discrete two-dimensional Toda lattices corresponding to simple Lie algebras of the $A$ and $C$ series.

Keywords: discrete Toda lattice, discrete exponential system, Darboux integrability, integral along characteristics

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation НШ-4833.2014.1
2010-220-01-077
Russian Foundation for Basic Research 14-01-00012_а


DOI: https://doi.org/10.4213/tmf8772

Full text: PDF file (561 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 182:2, 189–210

Bibliographic databases:

Document Type: Article
Received: 21.07.2014

Citation: S. V. Smirnov, “Darboux integrability of discrete two-dimensional Toda lattices”, TMF, 182:2 (2015), 231–255; Theoret. and Math. Phys., 182:2 (2015), 189–210

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    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. I. T. Habibullin, A. R. Khakimova, M. N. Poptsova, “On a method for constructing the Lax pairs for nonlinear integrable equations”, J. Phys. A-Math. Theor., 49:3 (2016), 035202  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. D. K. Demskoi, D. T. Tran, “Darboux integrability of determinant and equations for principal minors”, Nonlinearity, 29:7 (2016), 1973–1991  crossref  mathscinet  zmath  isi  elib  scopus
    3. Ismagil Habibullin, Mariya Poptsova, “Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings”, SIGMA, 13 (2017), 073, 26 pp.  mathnet  crossref
    4. W. Fu, “Direct linearisation of the discrete-time two-dimensional Toda lattices”, J. Phys. A-Math. Theor., 51:33 (2018), 334001  crossref  isi  scopus
    5. M. N. Poptsova, I. T. Habibullin, “Algebraic properties of quasilinear two-dimensional lattices connected with integrability”, Ufa Math. J., 10:3 (2018), 86–105  mathnet  crossref  isi
    6. S. V. Smirnov, “Factorization of Darboux–Laplace transformations for discrete hyperbolic operators”, Theoret. and Math. Phys., 199:2 (2019), 621–636  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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