Crank–Nicolson Fourier spectral methods for the space fractional nonlinear Schrödinger equation and its parameter estimation

International Journal of Computer Mathematics ◽

10.1080/00207160.2018.1434515 ◽

2018 ◽

Vol 96 (2) ◽

pp. 238-263 ◽

Author(s):

Hui Zhang ◽

Xiaoyun Jiang ◽

Chu Wang ◽

Shanzhen Chen

Keyword(s):

Parameter Estimation ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Spectral Methods ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation ◽

Fourier Spectral Methods ◽

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Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2015.12.042 ◽

2016 ◽

Vol 71 (11) ◽

pp. 2257-2271 ◽

Author(s):

Siwei Duo ◽

Yanzhi Zhang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Spectral Methods ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation ◽

Fourier Spectral Methods

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Efficient energy preserving Galerkin–Legendre spectral methods for fractional nonlinear Schrödinger equation with wave operator

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.10.013 ◽

2021 ◽

Author(s):

Dongdong Hu ◽

Wenjun Cai ◽

Xian-Ming Gu ◽

Yushun Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Spectral Methods ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Efficient Energy ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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Multi-peak solutions to fractional nonlinear Schrödinger equation with general nonlinearity

Complex Variables and Elliptic Equations ◽

10.1080/17476933.2021.1900138 ◽

2021 ◽

pp. 1-26

Author(s):

Xudong Shang ◽

Pei Ma ◽

Jihui Zhang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

General Nonlinearity ◽

Fractional Nonlinear Schrödinger Equation

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A Fast Conservative Scheme for the Space Fractional Nonlinear Schrödinger Equation with Wave Operator

Journal of Mathematical Study ◽

10.4208/jms.v54n4.21.06 ◽

2021 ◽

Vol 54 (4) ◽

pp. 407-426

Author(s):

MustafaAlmushaira & FeiLiu

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Conservative Scheme ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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Global existence and blowup on the energy space for the inhomogeneous fractional nonlinear Schrödinger equation

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2018323 ◽

2019 ◽

Vol 24 (7) ◽

pp. 3335-3356 ◽

Author(s):

Congming Peng ◽

◽

Dun Zhao ◽

Keyword(s):

Global Existence ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Energy Space ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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Multi-bump positive solutions of a fractional nonlinear Schrödinger equation in $\mathbb{R}^N$

Communications on Pure and Applied Analysis ◽

10.3934/cpaa.2016.15.413 ◽

2016 ◽

Vol 15 (2) ◽

pp. 413-428

Author(s):

Weiming Liu ◽

Lu Gan

Keyword(s):

Schrödinger Equation ◽

Positive Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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An energy-preserving Crank–Nicolson Galerkin spectral element method for the two dimensional nonlinear Schrödinger equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.05.025 ◽

2018 ◽

Vol 344 ◽

pp. 245-258 ◽

Author(s):

Haochen Li ◽

Zhenguo Mu ◽

Yushun Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Spectral Element Method ◽

Spectral Element ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

Element Method ◽

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Dynamical behavior and exact solutions for time-fractional nonlinear Schrödinger equation with parabolic law nonlinearity

Optik ◽

10.1016/j.ijleo.2020.165331 ◽

2020 ◽

Vol 222 ◽

pp. 165331

Author(s):

Cheng Chen ◽

Yaolin Jiang ◽

Zuolei Wang ◽

Juanjuan Wu

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Dynamical Behavior ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Parabolic Law ◽

Fractional Nonlinear Schrödinger Equation ◽

Parabolic Law Nonlinearity

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Vector optical soliton and periodic solutions of a coupled fractional nonlinear Schrödinger equation

Results in Physics ◽

10.1016/j.rinp.2020.103036 ◽

2020 ◽

Vol 17 ◽

pp. 103036 ◽

Author(s):

Ben-Hai Wang ◽

Peng-Hong Lu ◽

Chao-Qing Dai ◽

Yi-Xiang Chen

Keyword(s):

Schrödinger Equation ◽

Periodic Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Optical Soliton ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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On the solution of the fractional nonlinear Schrödinger equation

Physics Letters A ◽

10.1016/j.physleta.2007.06.071 ◽

2008 ◽

Vol 372 (5) ◽

pp. 553-558 ◽

Author(s):

S.Z. Rida ◽

H.M. El-Sherbiny ◽

A.A.M. Arafa

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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