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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 2, Pages 384–406 (Mi izv1404)  

This article is cited in 10 scientific papers (total in 10 papers)

Integrable differential equations and coverings of elliptic curves

I. V. Cherednik


Abstract: An algebraic theory is presented for differential equations with operator sheaf of elliptic type (in particular, with rational sheaf of operators); this theory includes local conservation laws, Bäcklund–Darboux transformations, and algebro-geometric (e.g., multisoliton) solutions.
Bibliography: 27 titles.

Full text: PDF file (2781 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1984, 22:2, 357–377

Bibliographic databases:

UDC: 517.9
MSC: Primary 58F07, 58F25, 35Q20; Secondary 35L65, 14K07, 14F05
Received: 29.03.1982

Citation: I. V. Cherednik, “Integrable differential equations and coverings of elliptic curves”, Izv. Akad. Nauk SSSR Ser. Mat., 47:2 (1983), 384–406; Math. USSR-Izv., 22:2 (1984), 357–377

Citation in format AMSBIB
\Bibitem{Che83}
\by I.~V.~Cherednik
\paper Integrable differential equations and coverings of elliptic curves
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 2
\pages 384--406
\mathnet{http://mi.mathnet.ru/izv1404}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=697302}
\zmath{https://zbmath.org/?q=an:0547.35109}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 22
\issue 2
\pages 357--377
\crossref{https://doi.org/10.1070/IM1984v022n02ABEH001448}


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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. M. Gel'fand, I. V. Cherednik, “The abstract Hamiltonian formalism for the classical Yang–Baxter bundles”, Russian Math. Surveys, 38:3 (1983), 1–22  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. V. Cherednik, “On the group-theoretical interpretation of Baker functions and $\tau$-functions”, Russian Math. Surveys, 38:6 (1983), 113–114  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. I. V. Cherednik, “Becklund–Darboux transformation for classical Yang–Baxter bundles”, Funct. Anal. Appl., 17:2 (1983), 155–157  mathnet  crossref  mathscinet  zmath  isi
    4. I. V. Cherednik, “Definition of functions for generalized affine Lie algebras”, Funct. Anal. Appl., 17:3 (1983), 243–245  mathnet  crossref  mathscinet  zmath  isi
    5. A. I. Bobenko, “Real algebrogeometric solutions of the Landau–Lifshits equation in prym theta functions”, Funct. Anal. Appl., 19:1 (1985), 5–17  mathnet  crossref  mathscinet  zmath  isi
    6. I. V. Cherednik, “Functional realizations of basis representations of factoring Lie groups and algebras”, Funct. Anal. Appl., 19:3 (1985), 193–206  mathnet  crossref  mathscinet  zmath  isi
    7. A. I. Bobenko, “Euler equations in the algebras $e(3)$ and $so(4)$. Isomorphisms of integrable cases”, Funct. Anal. Appl., 20:1 (1986), 53–56  mathnet  crossref  mathscinet  zmath  isi
    8. E. Barouch, A. S. Fokas, V. G. Papageorgiou, “The bi-Hamiltonian formulation of the Landau–Lifshiftz equation”, J Math Phys (N Y ), 29:12 (1988), 2628  crossref  mathscinet  zmath  adsnasa
    9. F.W. Nijhoff, V. Papageorgiou, “Lattice equations associated with the Landau-Lifschitz equations”, Physics Letters A, 141:5-6 (1989), 269  crossref
    10. R. F. Bikbaev, A. I. Bobenko, A. R. Its, “Landau–Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions”, Theoret. and Math. Phys., 178:2 (2014), 143–193  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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