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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 Applications of quantum theory to quantum optics 78A10 Physical optics 35B40 Asymptotic behavior of solutions of PDE 35B45 A priori estimates for solutions of PDE 35B41 Attractors (PDE)
##### References:
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