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Long-time behavior of solution for coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities. (English) Zbl 1181.35271

Summary: The Cauchy problem of coupled Ginzburg-Landau (GL) equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities is considered. The long-time behavior of solution is investigated using a series of sharp a priori estimates in phase space \(E_{1}\) and \(E_{2}\), respectively. The global strong attractor in \(E_{2}\) is proved by energy equation method, and its bound of dimension is shown.

MSC:

35Q56 Ginzburg-Landau equations
81V80 Quantum optics
78A10 Physical optics
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
35B41 Attractors
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