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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Explicit high-order structure-preserving algorithms for the two-dimensional fractional nonlinear Schrödinger equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2021.1940978 ◽

2021 ◽

pp. 1-28

Author(s):

Yayun Fu ◽

Yanhua Shi ◽

Yanmin Zhao

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Order Structure ◽

Two Dimensional ◽

High Order Structure ◽

Structure Preserving ◽

Fractional Nonlinear Schrödinger Equation

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Two novel classes of linear high-order structure-preserving schemes for the generalized nonlinear Schrödinger equation

Applied Mathematics Letters ◽

10.1016/j.aml.2020.106273 ◽

2020 ◽

Vol 104 ◽

pp. 106273 ◽

Author(s):

Xin Li ◽

Yuezheng Gong ◽

Luming Zhang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Order Structure ◽

High Order Structure ◽

Structure Preserving ◽

Nonlinear Schrödinger ◽

Generalized Nonlinear Schrödinger Equation

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High-Order Linearly Implicit Structure-Preserving Exponential Integrators for the Nonlinear Schrödinger Equation

Journal of Scientific Computing ◽

10.1007/s10915-021-01739-x ◽

2021 ◽

Vol 90 (1) ◽

Author(s):

Chaolong Jiang ◽

Jin Cui ◽

Xu Qian ◽

Songhe Song

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Exponential Integrators ◽

Structure Preserving ◽

Nonlinear Schrödinger

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High-order conservative schemes for the space fractional nonlinear Schrödinger equation

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.02.017 ◽

2021 ◽

Vol 165 ◽

pp. 248-269 ◽

Author(s):

Junjie Wang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Conservative Schemes ◽

Fractional Nonlinear Schrödinger Equation

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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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Linear High-Order Energy-Preserving Schemes for the Nonlinear Schrödinger Equation with Wave Operator Using the Scalar Auxiliary Variable Approach

Journal of Scientific Computing ◽

10.1007/s10915-021-01533-9 ◽

2021 ◽

Vol 88 (1) ◽

Author(s):

Xin Li ◽

Yuezheng Gong ◽

Luming Zhang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Auxiliary Variable ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Order Energy ◽

Variable Approach

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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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