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Uspekhi Mat. Nauk, 1991, Volume 46, Issue 3(279), Pages 3–48 (Mi umn4602)  

This article is cited in 34 scientific papers (total in 34 papers)

Algebraic constructions of integrable dynamical systems-extensions of the Volterra system

O. I. Bogoyavlenskii

Steklov Mathematical Institute, Russian Academy of Sciences

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English version:
Russian Mathematical Surveys, 1991, 46:3, 1–64

Bibliographic databases:

UDC: 539.2
MSC: 37K10, 45J05, 17B20, 45D05
Received: 26.11.1990

Citation: O. I. Bogoyavlenskii, “Algebraic constructions of integrable dynamical systems-extensions of the Volterra system”, Uspekhi Mat. Nauk, 46:3(279) (1991), 3–48; Russian Math. Surveys, 46:3 (1991), 1–64

Citation in format AMSBIB
\by O.~I.~Bogoyavlenskii
\paper Algebraic constructions of integrable dynamical systems-extensions of the Volterra system
\jour Uspekhi Mat. Nauk
\yr 1991
\vol 46
\issue 3(279)
\pages 3--48
\jour Russian Math. Surveys
\yr 1991
\vol 46
\issue 3
\pages 1--64

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    2. T. A. Ivanova, A. D. Popov, “Self-dual Yang–Mills fields in $d=4$ and integrable systems in $1\leq d\leq 3$”, Theoret. and Math. Phys., 102:3 (1995), 280–304  mathnet  crossref  mathscinet  zmath  isi
    3. T. Tokihiro, D. Takahashi, J. Matsukidaira, J. Satsuma, “From Soliton Equations to Integrable Cellular Automata through a Limiting Procedure”, Phys Rev Letters, 76:18 (1996), 3247  crossref  adsnasa  isi
    4. Kazuhiro Hikami, “Statistical Mechanical Interpretation of the Inverse Scattering Method: Level Dynamics for Exclusion Statistics”, Phys Rev Letters, 80:20 (1998), 4374  crossref  isi  elib
    5. Andrzej J. Maciejewski, Sasho I. Popov, “Invariants of homogeneous ordinary differential equations”, Reports on Mathematical Physics, 41:3 (1998), 287  crossref
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    12. N V Ustinov, “Darboux transformations, infinitesimal symmetries and conservation laws for the nonlocal two-dimensional Toda lattice”, J Phys A Math Gen, 35:32 (2002), 6963  crossref  mathscinet  zmath  adsnasa  isi  elib
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    15. R. Sahadevan, S. Rajakumar, “Bilinear, trilinear forms, and exact solution of certain fourth order integrable difference equations”, J Math Phys (N Y ), 49:3 (2008), 033517  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. O. I. Bogoyavlenskij, “Integrable Lotka-Volterra systems”, Reg Chaot Dyn, 13:6 (2008), 543  crossref  mathscinet  isi  elib
    17. V E Adler, V V Postnikov, “On vector analogs of the modified Volterra lattice”, J. Phys. A: Math. Theor, 41:45 (2008), 455203  crossref
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    21. Amerbaev V.M., Sharamok A.V., “Sintez nelineinykh otobrazhenii metodom Gaussa”, Izv. vuzov. Elektronika, 2009, no. 2(76), 51–55
    22. Yoshiaki Itoh, “A combinatorial method for the vanishing of the Poisson brackets of an integrable Lotka–Volterra system”, J. Phys. A: Math. Theor, 42:2 (2009), 025201  crossref
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    29. A.K. Svinin, “On some classes of discrete polynomials and ordinary difference equations”, J. Phys. A: Math. Theor, 47:15 (2014), 155201  crossref
    30. 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
    31. V.E. Adler, “Integrability test for evolutionary lattice equations of higher order”, Journal of Symbolic Computation, 2015  crossref
    32. 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
    33. V. E. Adler, A. B. Shabat, “Volterra chain and Catalan numbers”, JETP Letters, 108:12 (2018), 825–828  mathnet  crossref  crossref  isi  elib
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