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Russian Mathematical Surveys, 1997, Volume 52, Issue 5, Pages 1057–1116
DOI: https://doi.org/10.1070/RM1997v052n05ABEH002105
(Mi rm889)
 

This article is cited in 68 scientific papers (total in 69 papers)

Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds

S. P. Novikova, I. A. Dynnikovb

a University of Maryland
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Received: 08.09.1997
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 34B24, 34L40
Language: English
Original paper language: Russian
Citation: S. P. Novikov, I. A. Dynnikov, “Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds”, Russian Math. Surveys, 52:5 (1997), 1057–1116
Citation in format AMSBIB
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\by S.~P.~Novikov, I.~A.~Dynnikov
\paper Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds
\jour Russian Math. Surveys
\yr 1997
\vol 52
\issue 5
\pages 1057--1116
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Linking options:
  • https://www.mathnet.ru/eng/rm889
  • https://doi.org/10.1070/RM1997v052n05ABEH002105
  • https://www.mathnet.ru/eng/rm/v52/i5/p175
  • This publication is cited in the following 69 articles:
    1. I T Habibullin, K I Faizulina, A R Khakimova, “Laplace transformations and sine-Gordon type integrable PDE”, J. Phys. A: Math. Theor., 57:1 (2024), 015203  crossref
    2. A R Khakimova, K I Faizulina, “Reduction of the Laplace sequence and sine-Gordon type equations”, J. Phys. A: Math. Theor., 57:49 (2024), 495208  crossref
    3. Ufa Math. J., 13:2 (2021), 160–169  mathnet  crossref  isi
    4. Habibullin I., Khakimova A., “Integrable Boundary Conditions For the Hirota-Miwa Equation and Lie Algebras”, J. Nonlinear Math. Phys., 27:3 (2020), 393–413  crossref  isi
    5. Ekaterina Shemyakova, “Classification of Darboux transformations for operators of the form ∂x∂y+a∂x+b∂y+c”, Illinois J. Math., 64:1 (2020)  crossref
    6. Habibullin I.T., Khakimova A.R., “Discrete Exponential Type Systems on a Quad Graph, Corresponding to the Affine Lie Algebras a(N)(-1)((1) )”, J. Phys. A-Math. Theor., 52:36 (2019), 365202  crossref  isi
    7. David Hobby, Ekaterina Shemyakova, “Classification of Multidimensional Darboux Transformations: First Order and Continued Type”, SIGMA, 13 (2017), 010, 20 pp.  mathnet  crossref
    8. Li S. Shemyakova E. Voronov T., “Differential Operators on the Superline, Berezinians, and Darboux Transformations”, Lett. Math. Phys., 107:9 (2017), 1689–1714  crossref  mathscinet  zmath  isi  scopus  scopus
    9. A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Russian Math. Surveys, 71:5 (2016), 801–906  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. I. A. Dynnikov, “On a new discretization of complex analysis”, Russian Math. Surveys, 70:6 (2015), 1031–1050  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. N. Yu. Erokhovets, “Buchstaber invariant theory of simplicial complexes and convex polytopes”, Proc. Steklov Inst. Math., 286 (2014), 128–187  mathnet  crossref  crossref  isi  elib  elib
    12. P. G. Grinevich, S. P. Novikov, “Discrete SLn-connections and self-adjoint difference operators on two-dimensional manifolds”, Russian Math. Surveys, 68:5 (2013), 861–887  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  elib  elib
    13. Kh. K. Ishkin, “Conditions for localization of the limit spectrum of a model operator associated with the Orr–Sommerfeld equation”, Dokl. Math, 86:1 (2012), 549  crossref  mathscinet  zmath  isi  elib  elib  scopus
    14. Rustem Garifullin, Ismagil Habibullin, Marina Yangubaeva, “Affine and finite Lie algebras and integrable Toda field equations on discrete space-time”, SIGMA, 8 (2012), 062, 33 pp.  mathnet  crossref  mathscinet
    15. Proc. Steklov Inst. Math., 273 (2011), 238–251  mathnet  crossref  mathscinet  zmath  isi  elib
    16. Hugo M. Campos, Raúl Castillo-Pérez, Vladislav V. Kravchenko, “Construction and application of Bergman-type reproducing kernels for boundary and eigenvalue problems in the plane”, Complex Variables and Elliptic Equations, 2011, 1  crossref  mathscinet  isi  scopus  scopus
    17. V. E. Adler, A. I. Bobenko, Y. B. Suris, “Classification of Integrable Discrete Equations of Octahedron Type”, International Mathematics Research Notices, 2011  crossref  mathscinet  isi  scopus
    18. V. L. Vereshchagin, “Discrete Toda lattices and the Laplace method”, Theoret. and Math. Phys., 160:3 (2009), 1229–1237  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. A. A. Gaifullin, “A Minimal Triangulation of Complex Projective Plane Admitting a Chess Colouring of Four-Dimensional Simplices”, Proc. Steklov Inst. Math., 266 (2009), 29–48  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    20. Adam Doliwa, Maciej Nieszporski, “Darboux transformations for linear operators on two-dimensional regular lattices”, J Phys A Math Theor, 42:45 (2009), 454001  crossref  mathscinet  zmath  isi  elib  scopus  scopus
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