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The long-time 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) : 503-530. 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) : 1233-1252. doi: 10.3934/cpaa.2017060 |
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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) : 3027-3042. doi: 10.3934/dcdss.2021031 |
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Rolci Cipolatti, Otared Kavian. On a nonlinear Schrödinger equation modelling ultra-short laser pulses with a large noncompact global attractor. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 121-132. doi: 10.3934/dcds.2007.17.121 |
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Olivier Goubet, Ezzeddine Zahrouni. Global attractor for damped forced nonlinear logarithmic Schrödinger equations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (8) : 2933-2946. doi: 10.3934/dcdss.2020393 |
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Hongwei Wang, Amin Esfahani. On the Cauchy problem for a nonlocal nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022039 |
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Olivier Goubet, Wided Kechiche. Uniform attractor for non-autonomous nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2011, 10 (2) : 639-651. doi: 10.3934/cpaa.2011.10.639 |
[8] |
Guo Ben-Yu, Wang Zhong-Qing. Modified Chebyshev rational spectral method for the whole line. Conference Publications, 2003, 2003 (Special) : 365-374. 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) : 6943-6974. doi: 10.3934/dcds.2016102 |
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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) : 837-867. doi: 10.3934/eect.2021028 |
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Peter V. Gordon, Cyrill B. Muratov. Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source. Networks and Heterogeneous Media, 2012, 7 (4) : 767-780. doi: 10.3934/nhm.2012.7.767 |
[12] |
Brahim Alouini. Finite dimensional global attractor for a class of two-coupled nonlinear fractional Schrödinger equations. Evolution Equations and Control Theory, 2022, 11 (2) : 559-581. 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) : 4545-4573. doi: 10.3934/cpaa.2020206 |
[14] |
Jean-Paul Chehab, Pierre Garnier, Youcef Mammeri. Long-time behavior of solutions of a BBM equation with generalized damping. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 1897-1915. doi: 10.3934/dcdsb.2015.20.1897 |
[15] |
Annalisa Iuorio, Stefano Melchionna. Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3765-3788. 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) : 703-715. 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) : 93-106. doi: 10.3934/dcds.1999.5.93 |
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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) : 383-400. doi: 10.3934/dcds.1997.3.383 |
[19] |
Binhua Feng, Xiangxia Yuan. On the Cauchy problem for the Schrödinger-Hartree equation. Evolution Equations and Control Theory, 2015, 4 (4) : 431-445. doi: 10.3934/eect.2015.4.431 |
[20] |
Binhua Feng, Dun Zhao. On the Cauchy problem for the XFEL Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4171-4186. doi: 10.3934/dcdsb.2018131 |
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