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This article is cited in 9 scientific papers (total in 9 papers)
Characteristic features of the dynamics of the Ginzburg–Landau equation in a plane domain
A. Yu. Kolesova, N. Kh. Rozovb a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
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 $\mathrm{Re}\varkappa_1\to0$.
Received: 24.04.2000
Citation:
A. Yu. Kolesov, N. Kh. Rozov, “Characteristic features of the dynamics of the Ginzburg–Landau equation in a plane domain”, TMF, 125:2 (2000), 205–220; Theoret. and Math. Phys., 125:2 (2000), 1476–1488
Linking options:
https://www.mathnet.ru/eng/tmf664https://doi.org/10.4213/tmf664 https://www.mathnet.ru/eng/tmf/v125/i2/p205
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Abstract page: | 426 | Full-text PDF : | 182 | References: | 56 | First page: | 3 |
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