Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 264-273
Citer cet article
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/
@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},
year = {1982},
volume = {115},
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
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
%U http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a21/
%G ru
%F ZNSL_1982_115_a21
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.
