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Zapiski Nauchnykh Seminarov LOMI, 1982, Volume 115, Pages 264–273
(Mi znsl4058)
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This article is cited in 7 scientific papers (total in 8 papers)
Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations
L. A. Takhtadzhyan, L. D. Faddeev
Abstract:
One gives a simple and general derivation of the well-known connection between the geometric and the Hamiltonian approaches in the classical method of the inverse problem. Namely, for the case of a two-dimensional auxiliary problem and periodic boundary conditions it is explicitly shown how the existence of the classical $r$-matrix for the integrable equations leads to their representation in the form of the condition of zero curvature.
Citation:
L. A. Takhtadzhyan, L. D. Faddeev, “Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Zap. Nauchn. Sem. LOMI, 115, "Nauka", Leningrad. Otdel., Leningrad, 1982, 264–273; J. Soviet Math., 28:5 (1985), 800–806
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https://www.mathnet.ru/eng/znsl4058 https://www.mathnet.ru/eng/znsl/v115/p264
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Abstract page: | 339 | Full-text PDF : | 136 |
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