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Applicable Analysis
An International Journal
Volume 60, 1996 - Issue 1-2
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Original Articles

Regularity of the attractor for a weakly damped nonlinear schrödinger equation

Olivier Goubet Universite Paris-Sud, Orsay, 91405, France
Pages 99-119 | Received 01 Nov 1995, Published online: 02 May 2007

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A. I. Komech & E. A. Kopylova. (2022) On global attractors for 2D damped driven nonlinear Schrödinger equations. Applicable Analysis 101:15, pages 5490-5503.
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A. S. Shcherbina. (2003) Gevrey regularity of the global attractor for the dissipative Zakharov system . Dynamical Systems 18:3, pages 201-225.
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Ryan McConnell. (2022) Nonlinear smoothing for the periodic generalized nonlinear Schrödinger equation. Journal of Differential Equations 341, pages 353-379.
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Sevastos Diamantidis, Theodoros P. Horikis & Nikos I. Karachalios. (2021) Exciting extreme events in the damped and AC-driven NLS equation through plane-wave initial conditions. Chaos: An Interdisciplinary Journal of Nonlinear Science 31:5.
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PRASHANT GOYAL. (2019) GLOBAL ATTRACTOR FOR WEAKLY DAMPED, FORCED mKdV EQUATION BELOW ENERGY SPACE. Nagoya Mathematical Journal 241, pages 171-203.
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Wided Kechiche. (2021) Global attractor for a nonlinear Schrödinger equation with a nonlinearity concentrated in one point. Discrete & Continuous Dynamical Systems - S 14:8, pages 3027.
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Olivier Goubet & Ezzeddine Zahrouni. (2021) Global attractor for damped forced nonlinear logarithmic Schrödinger equations. Discrete & Continuous Dynamical Systems - S 14:8, pages 2933.
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Nikolaos Gialelis. (2020) Inviscid limit of linearly damped and forced nonlinear Schrodinger equations. Electronic Journal of Differential Equations 2020:01-132, pages 66.
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G. Fotopoulos, D.J. Frantzeskakis, N.I. Karachalios, P.G. Kevrekidis, V. Koukouloyannis & K. Vetas. (2020) Extreme wave events for a nonlinear Schrödinger equation with linear damping and Gaussian driving. Communications in Nonlinear Science and Numerical Simulation 82, pages 105058.
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G. Fotopoulos, N. I. Karachalios, V. Koukouloyannis & K. Vetas. (2019) The linearly damped nonlinear Schrödinger equation with localized driving: spatiotemporal decay estimates and the emergence of extreme wave events. Zeitschrift für angewandte Mathematik und Physik 71:1.
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Ming Wang & Jianhua Huang. (2019) Finite dimensionality of the global attractor for a fractional Schrödinger equation on . Applied Mathematics Letters 98, pages 432-437.
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Michael S. Jolly, Vincent R. Martinez, Tural Sadigov & Edriss S. Titi. (2018) A Determining Form for the Subcritical Surface Quasi-Geostrophic Equation. Journal of Dynamics and Differential Equations 31:3, pages 1457-1494.
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Lianbing She, Yangrong Li & Renhai Wang. (2018) Pullback-Forward Dynamics for Damped Schrödinger Equations with Time-Dependent Forcing. Discrete Dynamics in Nature and Society 2018, pages 1-14.
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Mostafa Abounouh, Hassan Al Moatassime & Abderrazak Chrifi. (2017) Existence of global attractor for one-dimensional weakly damped nonlinear Schrödinger equation with Dirac interaction and artificial boundary condition in half-line. Advances in Difference Equations 2017:1.
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Olivier Goubet & Ezzeddine Zahrouni. (2017) Finite dimensional global attractor for a fractional nonlinear Schrödinger equation. Nonlinear Differential Equations and Applications NoDEA 24:5.
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Caterina Calgaro, Olivier Goubet & Ezzeddine Zahrouni. (2017) Finite-dimensional global attractor for a semi-discrete fractional nonlinear Schrödinger equation. Mathematical Methods in the Applied Sciences 40:15, pages 5563-5574.
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Ibrahim Ekren, Igor Kukavica & Mohammed Ziane. (2017) Existence of invariant measures for the stochastic damped Schrödinger equation. Stochastics and Partial Differential Equations: Analysis and Computations 5:3, pages 343-367.
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Ibrahim Ekren, Igor Kukavica & Mohammed Ziane. (2017) Existence of invariant measures for some damped stochastic dispersive equations. Comptes Rendus Mathematique 355:6, pages 676-679.
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Wided Kechiche. (2017) Regularity of the global attractor for a nonlinear Schrödinger equation with a point defect. Communications on Pure & Applied Analysis 16:4, pages 1233-1252.
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Amna Dabaa & O. Goubet. (2016) Long time behavior of solutions to a Schrödinger-Poisson system in $R^3$. Communications on Pure and Applied Analysis 15:5, pages 1743-1756.
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Yanqiu Guo & Edriss S. Titi. (2015) On the backward behavior of some dissipative evolution equations. Physica D: Nonlinear Phenomena 306, pages 34-47.
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Michael S. Jolly, Tural Sadigov & Edriss S. Titi. (2015) A determining form for the damped driven nonlinear Schrödinger equation—Fourier modes case. Journal of Differential Equations 258:8, pages 2711-2744.
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Olivier Goubet & Marilena Poulou. (2014) Semi discrete weakly damped nonlinear Klein-Gordon Schrödinger system. Communications on Pure and Applied Analysis 13:4, pages 1525-1539.
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Marius Paicu, Geneviève Raugel & Andrey Rekalo. (2012) Regularity of the global attractor and finite-dimensional behavior for the second grade fluid equations. Journal of Differential Equations 252:6, pages 3695-3751.
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Emna Ezzoug, Wided Kechiche & Ezzeddine Zahrouni. (2011) Finite dimensional global attractor for a semi-discrete nonlinear Schrödinger equation with a point defect. Applied Mathematics and Computation 217:19, pages 7818-7830.
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Dong-long Li, Bo-ling Guo & Xu-hong Liu. (2011) Regularity of the attractor for 3-D complex Ginzburg-Landau equation. Acta Mathematicae Applicatae Sinica, English Series 27:2, pages 289-302.
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Olivier Goubet & Wided Kechiche. (2010) Uniform attractor for non-autonomous nonlinear Schrödinger equation. Communications on Pure and Applied Analysis 10:2, pages 639-651.
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Chaosheng Zhu, Chunlai Mu & Zhilin Pu. (2010) Attractor for the nonlinear Schrödinger equation with a nonlocal nonlinear term. Journal of Dynamical and Control Systems 16:4, pages 585-603.
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O. Goubet & L. Legry. (2010) Finite dimensional global attractor for a parametric nonlinear Schrödinger system with a trapping potential. Nonlinear Analysis: Theory, Methods & Applications 72:12, pages 4397-4406.
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Sergio Frigeri. (2009) Attractors for semilinear damped wave equations with an acoustic boundary condition. Journal of Evolution Equations 10:1, pages 29-58.
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O. Goubet & L. Molinet. (2009) Global attractor for weakly damped nonlinear Schrödinger equations in. Nonlinear Analysis: Theory, Methods & Applications 71:1-2, pages 317-320.
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Varga K. Kalantarov, Boris Levant & Edriss S. Titi. (2008) Gevrey Regularity for the Attractor of the 3D Navier–Stokes–Voight Equations. Journal of Nonlinear Science 19:2, pages 133-152.
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C. S. Zhu. (2008) Gevrey regularity of the attractor for the Sobolev-Galpern equation. Lobachevskii Journal of Mathematics 29:4, pages 264-270.
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Milena Stanislavova, Atanas Stefanov & Bixiang Wang. (2005) Asymptotic smoothing and attractors for the generalized Benjamin–Bona–Mahony equation on . Journal of Differential Equations 219:2, pages 451-483.
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Nikos I. Karachalios & Athanasios N. Yannacopoulos. (2005) Global existence and compact attractors for the discrete nonlinear Schrödinger equation. Journal of Differential Equations 217:1, pages 88-123.
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Jack K. Hale & Geneviève Raugel. (2003) Regularity, determining modes and Galerkin methods. Journal de Mathématiques Pures et Appliquées 82:9, pages 1075-1136.
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Olivier Goubet & Ricardo M.S. Rosa. (2002) Asymptotic Smoothing and the Global Attractor of a Weakly Damped KdV Equation on the Real Line. Journal of Differential Equations 185:1, pages 25-53.
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Zhang Xingyou. (2002) Asymptotic smoothing effect for a weakly damped forced equation of shallow water type. Nonlinear Analysis: Theory, Methods & Applications 50:6, pages 787-805.
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M Higuera, J Porter & E Knobloch. (2002) Heteroclinic dynamics in the nonlocal parametrically driven nonlinear Schrödinger equation. Physica D: Nonlinear Phenomena 162:3-4, pages 155-187.
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G. Raugel. 2002. 885 982 .
Edgar Knobloch & José M. Vega. 2002. Geometry, Mechanics, and Dynamics. Geometry, Mechanics, and Dynamics 181 222 .
Marcel Oliver & Edriss S. Titi. (2001) On the Domain of Analyticity for Solutions of Second Order Analytic Nonlinear Differential Equations. Journal of Differential Equations 174:1, pages 55-74.
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I D Chueshov. (2000) Analyticity of global attractors and determining nodes for a class of damped non-linear wave equations. Sbornik: Mathematics 191:10, pages 1541-1559.
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Guy Moebs & Roger Temam. (2000) Resolution of a stochastic weakly damped nonlinear Schrödinger equation by a multilevel numerical method. Journal of the Optical Society of America A 17:10, pages 1870.
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Olivier Goubet. (2000) Asymptotic Smoothing Effect for a Weakly Damped Nonlinear Schrodinger Equation in T2. Journal of Differential Equations 165:1, pages 96-122.
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Marcel Oliver & Edriss S Titi. (2000) Gevrey Regularity for the Attractor of a Partially Dissipative Model of Bénard Convection in a Porous Medium. Journal of Differential Equations 163:2, pages 292-311.
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Игорь Дмитриевич Чуешов & Igor Dmitrievich Chueshov. (2000) Аналитичность глобальных аттракторов и определяющие узлы для некоторого класса нелинейных волновых уравнений с демпфированиемAnalyticity of global attractors and determining nodes for a class of damped non-linear wave equations. Математический сборник Matematicheskii Sbornik 191:10, pages 119-136.
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Horst Lange & Bixiang Wang. (1999) Regularity of the global attractor for the Klein-Gordon-Schrödinger equation. Mathematical Methods in the Applied Sciences 22:17, pages 1535-1554.
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N. Akroune. (1999) Regularity of the attractor for a weakly damped nonlinear Schrödinger equation on R. Applied Mathematics Letters 12:3, pages 45-48.
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Bixiang Wang. (1998) Regularity of attractors for the Benjamin-Bona-Mahony equation. Journal of Physics A: Mathematical and General 31:37, pages 7635-7645.
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Ioana Moise, Ricardo Rosa & Xiaoming Wang. (1998) Attractors for non-compact semigroups via energy equations. Nonlinearity 11:5, pages 1369-1393.
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O. Goubet & I. Moise. (1998) Attractor for dissipative Zakharov system. Nonlinear Analysis: Theory, Methods & Applications 31:7, pages 823-847.
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O. Goubet. (1997) Regularity of the attractor for Schrödinger equation. Applied Mathematics Letters 10:1, pages 57-59.
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