Exponential Attractor For Coupled Ginzburg-Landau Equations

It is well known that exponentia1 attractor play an important role in the study oflong time behavior of solutions to nonlinear di?usion equations, and the easiest wayof obtaining an exponential attractor is by taking the intersection of an absorbing setwith an inertial manifold.In this paper, base on the Ref.[10], we further investigat thelong-time behavior of solution for coupled Ginzburg-Landau equations which describingBose-Einstein condensates and nonlinear optical waveguides and cavities with periodicinitial boundary, the existence of the exponential attractors, which include generalizedexponential attractor and (V₂,V₁)-type exponential attractor, are obtained by showingLipschitz continuous and the squeezing property.