Finite dimensional behavior for weakly damped driven Schrödinger equations. (English) Zbl 0659.35019

We study the long time behavior of nonlinear Schrödinger equations with a zero order dissipation when they are driven by an external force. We show that this behavior is described by an attractor which captures all the trajectories. One of our main results concerns the estimate of the uniform Lyapunov exponents on this attractor, which allows us to prove its finite dimensional character.


35G20 Nonlinear higher-order PDEs
35B40 Asymptotic behavior of solutions to PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
78A60 Lasers, masers, optical bistability, nonlinear optics
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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