O. I. Bogoyavlenskii, “Algebraic constructions of certain integrable equations”, Izv. Akad. Nauk SSSR Ser. Mat., 52:4 (1988), 712–739; Math. USSR-Izv., 33:1 (1989), 39

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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 4, Pages 712–739 (Mi izv1201)

This article is cited in 8 scientific papers (total in 8 papers)

Algebraic constructions of certain integrable equations

O. I. Bogoyavlenskii

Abstract: For differential equations in an arbitrary associative algebra, invariant constructions are presented that are connected with automorphisms of the algebra and admit a Lax representation. A Lax representation is found for a certain Hamiltonian integrodifferential equation, along with explicit formulas for a countable set of first integrals of it.
Bibliography: 13 titles

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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:1, 39–65

Bibliographic databases:

UDC: 517.91
MSC: Primary 45K05, 35Q20; Secondary 34C35, 35J10, 58F05
Received: 09.03.1988

Citation: O. I. Bogoyavlenskii, “Algebraic constructions of certain integrable equations”, Izv. Akad. Nauk SSSR Ser. Mat., 52:4 (1988), 712–739; Math. USSR-Izv., 33:1 (1989), 39–65

Citation in format AMSBIB

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\vol 52

\issue 4

\pages 712--739

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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=966981}

\zmath{https://zbmath.org/?q=an:0816.58019|0682.58024}

\transl

\jour Math. USSR-Izv.

\yr 1989

\vol 33

\issue 1

\pages 39--65

\crossref{https://doi.org/10.1070/IM1989v033n01ABEH000812}

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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:

O. I. Bogoyavlenskii, “A theorem on two commuting automorphisms, and integrable differential equations”, Math. USSR-Izv., 36:2 (1991), 263–279
O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–89
O. I. Bogoyavlenskii, “Breaking solitons. VI. Extension of systems of hydrodynamic type”, Math. USSR-Izv., 39:2 (1992), 959–973
A. S. Piskunov, “A (3+1)-dimensional equation admitting a Lax representation”, Russian Acad. Sci. Izv. Math., 40:1 (1993), 225–233
Theoret. and Math. Phys., 92:3 (1992), 1024–1031
Yuri B. Suris, “Integrable discretizations of the Bogoyavlensky lattices”, J Math Phys (N Y ), 37:8 (1996), 3982
Vassilios G. Papageorgiou, Frank W. Nijhoff, “On some integrable discrete-time systems associated with the Bogoyavlensky lattices”, Physica A: Statistical Mechanics and its Applications, 228:1-4 (1996), 172
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

Известия Академии наук СССР. Серия математическая

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