Characteristic features of the dynamics of the Ginzburg-Landau equation in a plane domain |
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Authors: | A. Yu. Kolesov N. Kh. Rosov |
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Affiliation: | (1) Yaroslavl State University, Yaroslavl, Russia;(2) Moscow State University, Moscow, Russia |
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Abstract: | We study the boundary value problem wt=ℵ0Δw+ℵ1w-ℵ2w|w|2,w|∂Ω0=0 in the domain Ω0={(x,y):0 ≤ x ≤ l1,0 ≤ y ≤ l2}. Here, w is a complex-valued function, Δ is the laplace operator, and ℵj, j=0,1,2, are complex constants withRe ℵj > 0. We show that under a rather general choice of the parameters l1 and l2, the number of stable invariant tori in the problem, as well as their dimensions, grows infinitely asRe ℵ0 → 0 andRe ℵ0 → 0. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 2, pp. 205–220, November, 2000. |
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