Regularity of the attractor for a weakly damped nonlinear Schrödinger equation on \(\mathbb{R}\)

DOI10.1016/S0893-9659(98)00170-0zbMath0937.35168MaRDI QIDQ1808523

N. Akroune

Publication date: 25 November 1999

Published in: Applied Mathematics Letters (Search for Journal in Brave)

zbMATH Keywords

global attractornonlinear Schrödinger equationweak dampinglong time behaviour

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (12)

Long time behavior of solutions to a Schrödinger-Poisson system in \(\mathbb R^3\) ⋮ Finite dimensional global attractor for a fractional nonlinear Schrödinger equation ⋮ Semi discrete weakly damped nonlinear Klein-Gordon Schrödinger system ⋮ Pullback-forward dynamics for damped Schrödinger equations with time-dependent forcing ⋮ Asymptotic smoothing effect of solutions to Davey-Stewartson systems on the whole plane ⋮ Finite dimensional global attractor for a semi-discrete nonlinear Schrödinger equation with a point defect ⋮ Finite dimensionality of the global attractor for a fractional Schrödinger equation on \(\mathbb{R}\) ⋮ Unnamed Item ⋮ Global attractor for weakly damped nonlinear Schrödinger equations in \(L^2(\mathbb R)\) ⋮ Global attractor for a nonlinear Schrödinger equation with a nonlinearity concentrated in one point ⋮ Asymptotic smoothing effect for a weakly damped nonlinear Schrödinger equation in \(\mathbb{T}^2\) ⋮ Nonlinear smoothing for the periodic generalized nonlinear Schrödinger equation

Cites Work

• Unnamed Item
• Finite dimensional behavior for weakly damped driven Schrödinger equations
• Infinite-dimensional dynamical systems in mechanics and physics
• Global attractors for damped semilinear wave equations.
• On a variation of the box-counting method for the numerical determination of the fractal dimension of a subset in 2D space
• Regularity of the attractor for a weakly damped nonlinear schrödinger equation

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