Finite dimensional behavior for weakly damped driven Schrödinger equations
DOI10.1016/S0294-1449(16)30343-2zbMath0659.35019MaRDI QIDQ1112239
Publication date: 1988
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIHPC_1988__5_4_365_0
attractornonlinear Schrödinger equationslong time behaviorexternal forceuniform Lyapunov exponentszero order dissipation
Asymptotic behavior of solutions to PDEs (35B40) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Nonlinear higher-order PDEs (35G20) Lasers, masers, optical bistability, nonlinear optics (78A60) Partial differential equations of mathematical physics and other areas of application (35Q99) Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena (76A99)
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Cites Work
- Attractors for damped nonlinear hyperbolic equations
- Low-dimensional chaos in a driven damped nonlinear Schrödinger equation
- Dimension of the attractors associated to the Ginzburg-Landau partial differential equation
- Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time
- Infinite-dimensional dynamical systems in mechanics and physics
- Non-linear semi-groups
- Nonexistence of Global Solutions to the Cauchy Problem for the Damped Nonlinear Schrödinger Equations
- Attractors representing turbulent flows
- On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
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