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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 125, Number 2, Pages 205–220
DOI: https://doi.org/10.4213/tmf664
(Mi tmf664)
 

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
Full-text PDF (273 kB) Citations (9)
References:
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
English version:
Theoretical and Mathematical Physics, 2000, Volume 125, Issue 2, Pages 1476–1488
DOI: https://doi.org/10.1007/BF02551008
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 125
\issue 2
\pages 1476--1488
\crossref{https://doi.org/10.1007/BF02551008}
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  • https://www.mathnet.ru/eng/tmf/v125/i2/p205
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:426
    Full-text PDF :182
    References:56
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