Geodesic
Integrable dynamical systems associated with the KdV equation
Izvestiya. Mathematics, Tome 31 (1988) no. 3, pp. 435-454 
O. I. Bogoyavlenskii. Integrable dynamical systems associated with the KdV equation. Izvestiya. Mathematics, Tome 31 (1988) no. 3, pp. 435-454. http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a0/
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     title = {Integrable dynamical systems associated with the {KdV} equation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Moser J., “Three Integrable Hamiltonian Systems Connected with Isospectral Deformations”, Adv. in Math., 16 (1975), 197–220 | DOI | MR | Zbl

[2] Bogoyavlenskii O. I., “Nekotorye konstruktsii integriruemykh dinamicheskikh sistem”, Izv. AN SSSR. Ser. matem., 51:4 (1987), 737–767 | MR

[3] Ablowitz N. J., Kaup D. J., Newell A. C., Segur H., “Nonlinear evolution equation of physical significance”, Phys. Rev. Letters, 32 (1973), 125–130 | DOI | MR

[4] Lax P., “Almost periodic behavior of nonlinear waves”, Adv. in Math., 16 (1975), 368–379 | DOI | MR | Zbl

[5] Kac M., van Moerbeke P., “On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices”, Adv. in Math., 16 (1975), 160–169 | DOI | MR | Zbl

[6] Manakov S. V., “O polnoi integriruemosti i stokhastizatsii v diskretnykh dinamicheskikh sistemakh”, ZhETF, 67:2 (1974), 543–555 | MR

[7] Bogoyavlensky O. I., “On perturbations of the periodic Toda lattice”, Comm. in Math. Phys., 51 (1976), 201–209 | DOI | MR

[8] Toda M., Theory of nonlinear lattices, Springer-Verlag, Berlin, New York, Heidelberg, 1981 | MR | Zbl

[9] Burbaki H., Gruppy i algebry Li, eds. A. I. Kostrikin, Mir, M., 1972 ; | MR | Zbl