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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:
35Q56Ginzburg-Landau equations
81V80Applications of quantum theory to quantum optics
78A10Physical optics
35B40Asymptotic behavior of solutions of PDE
35B45A priori estimates for solutions of PDE
35B41Attractors (PDE)
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