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The longtime behaviour for nonlinear Schrödinger equation and its rational pseudospectral approximation
1.  Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China 
[1] 
Olivier Goubet. Approximate inertial manifolds for a weakly damped nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 1997, 3 (4) : 503530. doi: 10.3934/dcds.1997.3.503 
[2] 
Wided Kechiche. Regularity of the global attractor for a nonlinear Schrödinger equation with a point defect. Communications on Pure and Applied Analysis, 2017, 16 (4) : 12331252. doi: 10.3934/cpaa.2017060 
[3] 
Wided Kechiche. Global attractor for a nonlinear Schrödinger equation with a nonlinearity concentrated in one point. Discrete and Continuous Dynamical Systems  S, 2021, 14 (8) : 30273042. doi: 10.3934/dcdss.2021031 
[4] 
Rolci Cipolatti, Otared Kavian. On a nonlinear Schrödinger equation modelling ultrashort laser pulses with a large noncompact global attractor. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 121132. doi: 10.3934/dcds.2007.17.121 
[5] 
Olivier Goubet, Ezzeddine Zahrouni. Global attractor for damped forced nonlinear logarithmic Schrödinger equations. Discrete and Continuous Dynamical Systems  S, 2021, 14 (8) : 29332946. doi: 10.3934/dcdss.2020393 
[6] 
Hongwei Wang, Amin Esfahani. On the Cauchy problem for a nonlocal nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems  B, 2022, 27 (12) : 71857206. doi: 10.3934/dcdsb.2022039 
[7] 
Olivier Goubet, Wided Kechiche. Uniform attractor for nonautonomous nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2011, 10 (2) : 639651. doi: 10.3934/cpaa.2011.10.639 
[8] 
Guo BenYu, Wang ZhongQing. Modified Chebyshev rational spectral method for the whole line. Conference Publications, 2003, 2003 (Special) : 365374. doi: 10.3934/proc.2003.2003.365 
[9] 
Hiroyuki Hirayama, Mamoru Okamoto. Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 69436974. doi: 10.3934/dcds.2016102 
[10] 
Phan Van Tin. On the Cauchy problem for a derivative nonlinear Schrödinger equation with nonvanishing boundary conditions. Evolution Equations and Control Theory, 2022, 11 (3) : 837867. doi: 10.3934/eect.2021028 
[11] 
Peter V. Gordon, Cyrill B. Muratov. Selfsimilarity and longtime behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source. Networks and Heterogeneous Media, 2012, 7 (4) : 767780. doi: 10.3934/nhm.2012.7.767 
[12] 
Brahim Alouini. Finite dimensional global attractor for a class of twocoupled nonlinear fractional Schrödinger equations. Evolution Equations and Control Theory, 2022, 11 (2) : 559581. doi: 10.3934/eect.2021013 
[13] 
Brahim Alouini. Finite dimensional global attractor for a damped fractional anisotropic Schrödinger type equation with harmonic potential. Communications on Pure and Applied Analysis, 2020, 19 (9) : 45454573. doi: 10.3934/cpaa.2020206 
[14] 
JeanPaul Chehab, Pierre Garnier, Youcef Mammeri. Longtime behavior of solutions of a BBM equation with generalized damping. Discrete and Continuous Dynamical Systems  B, 2015, 20 (7) : 18971915. doi: 10.3934/dcdsb.2015.20.1897 
[15] 
Annalisa Iuorio, Stefano Melchionna. Longtime behavior of a nonlocal CahnHilliard equation with reaction. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 37653788. doi: 10.3934/dcds.2018163 
[16] 
Paolo Antonelli, Daniel Marahrens, Christof Sparber. On the Cauchy problem for nonlinear Schrödinger equations with rotation. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 703715. doi: 10.3934/dcds.2012.32.703 
[17] 
Nakao Hayashi, Elena I. Kaikina, Pavel I. Naumkin. Large time behavior of solutions to the generalized derivative nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 93106. doi: 10.3934/dcds.1999.5.93 
[18] 
Nakao Hayashi, Pavel I. Naumkin. Asymptotic behavior in time of solutions to the derivative nonlinear Schrödinger equation revisited. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 383400. doi: 10.3934/dcds.1997.3.383 
[19] 
Vladimir Varlamov. Eigenfunction expansion method and the longtime asymptotics for the damped Boussinesq equation. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 675702. doi: 10.3934/dcds.2001.7.675 
[20] 
Binhua Feng, Xiangxia Yuan. On the Cauchy problem for the SchrödingerHartree equation. Evolution Equations and Control Theory, 2015, 4 (4) : 431445. doi: 10.3934/eect.2015.4.431 
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