Veselov-Novikov hierarchy of equations, and integrable deformations of minimal Lagrangian tori in~$\mathbb CP^2$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 1 (2004), pp. 38-46
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We associate a periodic two-dimensional Schrödinger operator to every Lagrangian torus in $\mathbb CP^2$ and define the spectral curve of a torus as the Floquet spectrum on this operator on the zero energy level. In this event minimal Lagrangian tori correspond to potential operators. We show that the Novikov–Veselov hierarchy of equations induces integrable deformations of a minimal Lagrangian torus in $\mathbb CP^2$ preserving the spectral curve.
@article{SEMR_2004_1_a3,
author = {A. E. Mironov},
title = {Veselov-Novikov hierarchy of equations, and integrable deformations of minimal {Lagrangian} tori in~$\mathbb CP^2$},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {38--46},
publisher = {mathdoc},
volume = {1},
year = {2004},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SEMR_2004_1_a3/}
}
TY - JOUR AU - A. E. Mironov TI - Veselov-Novikov hierarchy of equations, and integrable deformations of minimal Lagrangian tori in~$\mathbb CP^2$ JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2004 SP - 38 EP - 46 VL - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SEMR_2004_1_a3/ LA - ru ID - SEMR_2004_1_a3 ER -
%0 Journal Article %A A. E. Mironov %T Veselov-Novikov hierarchy of equations, and integrable deformations of minimal Lagrangian tori in~$\mathbb CP^2$ %J Sibirskie èlektronnye matematičeskie izvestiâ %D 2004 %P 38-46 %V 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/SEMR_2004_1_a3/ %G ru %F SEMR_2004_1_a3
A. E. Mironov. Veselov-Novikov hierarchy of equations, and integrable deformations of minimal Lagrangian tori in~$\mathbb CP^2$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 1 (2004), pp. 38-46. http://geodesic.mathdoc.fr/item/SEMR_2004_1_a3/