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

MustafaAlmushaira & FeiLiu

doi:10.4208/jms.v54n4.21.06

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

Download Full-text

A linearly implicit conservative scheme for the fractional nonlinear Schrödinger equation with wave operator

International Journal of Computer Mathematics ◽

10.1080/00207160.2015.1016924 ◽

2015 ◽

Vol 93 (7) ◽

pp. 1103-1118 ◽

Cited By ~ 16

Author(s):

Maohua Ran ◽

Chengjian Zhang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Conservative Scheme ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

Download Full-text

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

Download Full-text

A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator

Applied Mathematics and Computation ◽

10.1016/j.amc.2021.126234 ◽

2021 ◽

Vol 404 ◽

pp. 126234

Author(s):

Yuna Yang ◽

Hongwei Li ◽

Xu Guo

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Conservative Scheme ◽

Nonlinear Schrödinger

Download Full-text

A fourth-order difference scheme for the fractional nonlinear Schrödinger equation with wave operator

Applicable Analysis ◽

10.1080/00036811.2020.1829600 ◽

2020 ◽

pp. 1-17

Author(s):

Kejia Pan ◽

Jiali Zeng ◽

Dongdong He ◽

Saiyan Zhang

Keyword(s):

Schrödinger Equation ◽

Difference Scheme ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Order Difference ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

Download Full-text

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 ◽

High Order ◽

Nonlinear Schrödinger ◽

Order Energy ◽

Variable Approach

Download Full-text

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

Download Full-text

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 ◽

Cited By ~ 1

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

Download Full-text

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

Download Full-text

A new conservative fourth-order accurate difference scheme for the nonlinear Schrödinger equation with wave operator

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.11.005 ◽

2021 ◽

Author(s):

Labidi Samira ◽

Khaled Omrani

Keyword(s):

Schrödinger Equation ◽

Difference Scheme ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

Download Full-text

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

Download Full-text