Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 264-273
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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.
@article{ZNSL_1982_115_a21,
author = {L. A. Takhtadzhyan and L. D. Faddeev},
title = {Simple connection between the geometric and the {Hamiltonian} representations of integrable nonlinear equations},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {264--273},
publisher = {mathdoc},
volume = {115},
year = {1982},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a21/}
}
TY - JOUR AU - L. A. Takhtadzhyan AU - L. D. Faddeev TI - Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations JO - Zapiski Nauchnykh Seminarov POMI PY - 1982 SP - 264 EP - 273 VL - 115 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a21/ LA - ru ID - ZNSL_1982_115_a21 ER -
%0 Journal Article %A L. A. Takhtadzhyan %A L. D. Faddeev %T Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations %J Zapiski Nauchnykh Seminarov POMI %D 1982 %P 264-273 %V 115 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a21/ %G ru %F ZNSL_1982_115_a21
L. A. Takhtadzhyan; L. D. Faddeev. Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 264-273. http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a21/