This article is cited in 22 scientific papers (total in 22 papers)
Integrable dynamical systems associated with the KdV equation
O. I. Bogoyavlenskii
An isospectral deformation representation is constructed for a countable set of dynamical systems with a quadratic nonlinearity, which become the Korteweg–de Vries equation in the continuum limit. Integrable reductions of certain dynamical systems with an arbitrary degree of nonlinearity are obtained. The dynamics of the components of the scattering matrix are integrated for these infinitedimensional dynamical systems. An isospectral deformation representation is indicated for certain nonhomogeneous finite-dimensional dynamical systems. A new construction of integrable dynamical systems associated with simple Lie algebras and generalizing the discrete KdV equations is found.
Bibliography: 9 titles.
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Mathematics of the USSR-Izvestiya, 1988, 31:3, 435–454
MSC: Primary 58F07; Secondary 35Q20, 39A12
O. I. Bogoyavlenskii, “Integrable dynamical systems associated with the KdV equation”, Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987), 1123–1141; Math. USSR-Izv., 31:3 (1988), 435–454
Citation in format AMSBIB
\paper Integrable dynamical systems associated with the KdV equation
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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