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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 2, Pages 243–266 (Mi izv1179)  

This article is cited in 13 scientific papers (total in 13 papers)

The Lax representation with a spectral parameter for certain dynamical systems

O. I. Bogoyavlenskii


Abstract: It is shown that all dynamical systems forming a countable set of integrable discretizations of the KdV equation admit a Lax representation with a spectral parameter. Continuous limits of Fermi–Pasta–Ulam lattices are investigated, and a connection is established between them and the linear Tricomi equation.
Bibliography: 11 titles.

Full text: PDF file (2556 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1989, 32:2, 245–268

Bibliographic databases:

UDC: 517.91
MSC: Primary 34C35, 35Q20, 58F05; Secondary 35M05, 82A68
Received: 20.11.1987

Citation: O. I. Bogoyavlenskii, “The Lax representation with a spectral parameter for certain dynamical systems”, Izv. Akad. Nauk SSSR Ser. Mat., 52:2 (1988), 243–266; Math. USSR-Izv., 32:2 (1989), 245–268

Citation in format AMSBIB
\Bibitem{Bog88}
\by O.~I.~Bogoyavlenskii
\paper The Lax representation with a~spectral parameter for certain dynamical systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 2
\pages 243--266
\mathnet{http://mi.mathnet.ru/izv1179}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=941676}
\zmath{https://zbmath.org/?q=an:0695.35150|0672.35073}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 32
\issue 2
\pages 245--268
\crossref{https://doi.org/10.1070/IM1989v032n02ABEH000757}


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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. O. I. Bogoyavlenskii, “Algebraic constructions of certain integrable equations”, Math. USSR-Izv., 33:1 (1989), 39–65  mathnet  crossref  mathscinet  zmath
    2. O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–89  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Solomon J. Alber, “Associated integrable systems”, J Math Phys (N Y ), 32:4 (1991), 916  crossref  mathscinet  zmath
    4. O. I. Bogoyavlenskii, “Algebraic constructions of integrable dynamical systems-extensions of the Volterra system”, Russian Math. Surveys, 46:3 (1991), 1–64  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. O. I. Bogoyavlenskii, “Breaking solitons. V. Systems of hydrodynamic type”, Math. USSR-Izv., 38:3 (1992), 439–454  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Martin Bordemann, Jens Hoppe, “The dynamics of relativistic membranes. Reduction to 2-dimensional fluid dynamics”, Physics Letters B, 317:3 (1993), 315  crossref
    7. Jens Hoppe, “r-Functions with quasi-dynamical spectral parameter”, Lett Math Phys, 31:4 (1994), 255  crossref  mathscinet  zmath  isi
    8. A. S. Osipov, “Discrete analog of the Korteweg–de Vries (KdV) equation: Integration by the method of the inverse problem”, Math. Notes, 56:6 (1994), 1312–1314  mathnet  crossref  mathscinet  zmath  isi
    9. Jens Hoppe, Q.-Han Park, “Infinite charge algebra of gravitational instantons”, Physics Letters B, 321:4 (1994), 333  crossref
    10. Martin Bordemann, Jens Hoppe, “The dynamics of relativistic membranes. II: Nonlinear waves and covariantly reduced membrane equations”, Physics Letters B, 325:3-4 (1994), 359  crossref
    11. 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
    12. Yuri B. Suris, “Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices”, J Math Phys (N Y ), 38:8 (1997), 4179  crossref  mathscinet  zmath  adsnasa
    13. A Dimakis, F Müller-Hoissen, J Phys A Math Gen, 34:43 (2001), 9163  crossref  mathscinet  zmath  adsnasa
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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