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Izv. Akad. Nauk SSSR Ser. Mat., 1990, Volume 54, Issue 2, Pages 258–274 (Mi izv1093)  

This article is cited in 4 scientific papers (total in 4 papers)

A theorem on two commuting automorphisms, and integrable differential equations

O. I. Bogoyavlenskii


Abstract: Constructions are found for differential equations in an arbitrary continuous associative algebra $\mathfrak A$ that admit an equivalent Lax representation (with spectral parameter) in the space of linear operators acting on $\mathfrak A$. The constructions use commuting automorphisms of $\mathfrak A$. Applications of the main construction are indicated for the construction of integrable Euler equations in the direct sum of the Lie algebras $\operatorname{gl}(n,R)$ and $\operatorname{so}(n,R)$. Constructions are presented for matrix differential equations admitting a Lax representation with several spectral parameters.

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English version:
Mathematics of the USSR-Izvestiya, 1991, 36:2, 263–279

Bibliographic databases:

UDC: 539.2
MSC: Primary 58F07; Secondary 35Q20, 70H05
Received: 21.09.1989

Citation: O. I. Bogoyavlenskii, “A theorem on two commuting automorphisms, and integrable differential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 54:2 (1990), 258–274; Math. USSR-Izv., 36:2 (1991), 263–279

Citation in format AMSBIB
\Bibitem{Bog90}
\by O.~I.~Bogoyavlenskii
\paper A~theorem on two commuting automorphisms, and integrable differential equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1990
\vol 54
\issue 2
\pages 258--274
\mathnet{http://mi.mathnet.ru/izv1093}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1062513}
\zmath{https://zbmath.org/?q=an:0716.58018|0699.58041}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..36..263B}
\transl
\jour Math. USSR-Izv.
\yr 1991
\vol 36
\issue 2
\pages 263--279
\crossref{https://doi.org/10.1070/IM1991v036n02ABEH002021}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. O. I. Bogoyavlenskii, “Euler equations on finite-dimensional Lie coalgebras, arising in problems of mathematical physics”, Russian Math. Surveys, 47:1 (1992), 117–189  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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