Characteristic features of the dynamics of the Ginzburg--Landau equation in a plane domain
Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 2, pp. 205-220
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We study the boundary value problem $w_t=\varkappa_0\Delta w+\varkappa_1w-\varkappa_2w|w|^2$, $w|_{\partial\Omega_0}=0$ in the domain $\Omega_0=\bigl\{(x,y)\:0\leq x\leq l_1,0\leq y\leq l_2\bigr\}$. Here, $w$ is a complex-valued function, $\Delta$ is the Laplace operator, and $\varkappa_j$, $j=0,1,2$, are complex constants with $\mathrm{Re}\varkappa_j>0$. We show that under a rather general choice of the parameters $l_1$ and $l_2$, the number of stable invariant tori in the problem, as well as their dimensions, grows infinitely as $\mathrm{Re}\varkappa_0\to0$ and $\mathrm{Re}\varkappa_1\to0$.
@article{TMF_2000_125_2_a1,
author = {A. Yu. Kolesov and N. Kh. Rozov},
title = {Characteristic features of the dynamics of the {Ginzburg--Landau} equation in a plane domain},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {205--220},
publisher = {mathdoc},
volume = {125},
number = {2},
year = {2000},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a1/}
}
TY - JOUR AU - A. Yu. Kolesov AU - N. Kh. Rozov TI - Characteristic features of the dynamics of the Ginzburg--Landau equation in a plane domain JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2000 SP - 205 EP - 220 VL - 125 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a1/ LA - ru ID - TMF_2000_125_2_a1 ER -
%0 Journal Article %A A. Yu. Kolesov %A N. Kh. Rozov %T Characteristic features of the dynamics of the Ginzburg--Landau equation in a plane domain %J Teoretičeskaâ i matematičeskaâ fizika %D 2000 %P 205-220 %V 125 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a1/ %G ru %F TMF_2000_125_2_a1
A. Yu. Kolesov; N. Kh. Rozov. Characteristic features of the dynamics of the Ginzburg--Landau equation in a plane domain. Teoretičeskaâ i matematičeskaâ fizika, Tome 125 (2000) no. 2, pp. 205-220. http://geodesic.mathdoc.fr/item/TMF_2000_125_2_a1/