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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.
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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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\by O.~I.~Bogoyavlenskii
\paper Algebraic constructions of certain integrable equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\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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This publication is cited in the following articles:
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O. I. Bogoyavlenskii, “A theorem on two commuting automorphisms, and integrable differential equations”, Math. USSR-Izv., 36:2 (1991), 263–279
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O. I. Bogoyavlenskii, “Breaking solitons in $2+1$-dimensional integrable equations”, Russian Math. Surveys, 45:4 (1990), 1–89
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O. I. Bogoyavlenskii, “Breaking solitons. VI. Extension of systems of hydrodynamic type”, Math. USSR-Izv., 39:2 (1992), 959–973
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A. S. Piskunov, “A (3+1)-dimensional equation admitting a Lax representation”, Russian Acad. Sci. Izv. Math., 40:1 (1993), 225–233
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Theoret. and Math. Phys., 92:3 (1992), 1024–1031
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Yuri B. Suris, “Integrable discretizations of the Bogoyavlensky lattices”, J Math Phys (N Y ), 37:8 (1996), 3982
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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
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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
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