Global attractor for a class of coupled nonlinear Schrödinger equations. (English) Zbl 1260.35205
Summary: In this paper, the long time behavior of solution for a class of coupled nonlinear Schrödinger equation with zero order dissipation is studied. We first construct the global weak attractor for this system in \(H^2_{\text{per}}(\Omega)\times H^2_{\text{per}}(\Omega)\). Then, by exact analysis of the energy equation, we shown that the global weak attractor is actually the global strong attractor in \(H^2_{\text{per}}(\Omega)\times H^2_{\text{per}}(\Omega)\). We also estimate the uniform Lyapunov exponents on the attractor, which allows us to prove its finite dimensional property.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35B41 | Attractors |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
coupled nonlinear Schrödinger equations; global attractor; absorbing set; fractal dimensionReferences:
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