A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schrödinger equation

Journal of Computational Dynamics ◽

10.3934/jcd.2019018 ◽

2019 ◽

Vol 6 (2) ◽

pp. 361-383

Author(s):

Yuto Miyatake ◽

◽

Tai Nakagawa ◽

Tomohiro Sogabe ◽

Shao-Liang Zhang ◽

...

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Implicit Scheme ◽

Structure Preserving ◽

Nonlinear Schrödinger ◽

Pseudo Spectral ◽

Fractional Nonlinear Schrödinger Equation

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High-order structure-preserving algorithms for the multi-dimensional fractional nonlinear Schrödinger equation based on the SAV approach

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2020.12.025 ◽

2020 ◽

Author(s):

Yayun Fu ◽

Dongdong Hu ◽

Yushun Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Order Structure ◽

High Order Structure ◽

Structure Preserving ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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A linearly implicit structure-preserving Fourier pseudo-spectral scheme for the damped nonlinear Schrödinger equation in three dimensions

Advances in Computational Mathematics ◽

10.1007/s10444-020-09781-3 ◽

2020 ◽

Vol 46 (2) ◽

Author(s):

Chaolong Jiang ◽

Yongzhong Song ◽

Yushun Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Three Dimensions ◽

Structure Preserving ◽

Nonlinear Schrödinger ◽

Pseudo Spectral

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On the L ∞ convergence of a conservative Fourier pseudo‐spectral method for the space fractional nonlinear Schrödinger equation

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22599 ◽

2020 ◽

Author(s):

Zhuangzhi Xu ◽

Wenjun Cai ◽

Chaolong Jiang ◽

Yushun Wang

Keyword(s):

Schrödinger Equation ◽

Spectral Method ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Pseudo Spectral Method ◽

Pseudo Spectral ◽

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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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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