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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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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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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On convergence of a structure preserving difference scheme for two-dimensional space-fractional nonlinear Schrödinger equation and its fast implementation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.06.018 ◽

2021 ◽

Vol 98 ◽

pp. 10-23

Author(s):

Dongdong Hu ◽

Yuezheng Gong ◽

Yushun Wang

Keyword(s):

Schrödinger Equation ◽

Difference Scheme ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Dimensional Space ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Structure Preserving ◽

Fast Implementation ◽

Fractional 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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Bifurcation and new exact traveling wave solutions to time-space coupled fractional nonlinear Schrödinger equation

Physics Letters A ◽

10.1016/j.physleta.2021.127217 ◽

2021 ◽

Vol 395 ◽

pp. 127217

Author(s):

Tianyong Han ◽

Zhao Li ◽

Xue Zhang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Traveling Wave ◽

Schrodinger Equation ◽

Traveling Wave Solutions ◽

Nonlinear Schrodinger Equation ◽

Exact Traveling Wave Solutions ◽

Wave Solutions ◽

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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Local absorbing boundary conditions for two‐dimensional nonlinear Schrödinger equation with wave operator on unbounded domain

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7703 ◽

2021 ◽

Author(s):

Hongwei Li

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Nonlinear Schrödinger Equation ◽

Unbounded Domain ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Absorbing Boundary Conditions ◽

Two Dimensional ◽

Absorbing Boundary

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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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