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

Wave Operator ◽

Schrodinger Equation ◽

Auxiliary Variable ◽

High Order ◽

Nonlinear Schrödinger ◽

Order Energy ◽

Variable Approach

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 ◽

Wave Operator ◽

Schrodinger Equation ◽

Fractional Nonlinear Schrödinger Equation

Conservative Scheme ◽

Nonlinear Schrödinger ◽

Stabilization of high-order solutions of the cubic nonlinear Schrödinger equation

Physical Review E ◽

10.1103/physreve.75.046609 ◽

2007 ◽

Vol 75 (4) ◽

Cited By ~ 20

Author(s):

Adrian Alexandrescu ◽

Gaspar D. Montesinos ◽

Víctor M. Pérez-García

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Cubic Nonlinear Schrödinger Equation

High Order ◽

Nonlinear Schrödinger ◽

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 ◽

Fourth Order ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrödinger

Integrability and dark soliton solutions for a high-order variable coefficients nonlinear Schrödinger equation

Applied Mathematics Letters ◽

10.1016/j.aml.2019.01.029 ◽

2019 ◽

Vol 93 ◽

pp. 29-33 ◽

Cited By ~ 6

Author(s):

Qian-Min Huang

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Dark Soliton ◽

Variable Coefficients ◽

High Order ◽

Nonlinear Schrödinger ◽

Order Variable

NLSEmagic: Nonlinear Schrödinger equation multi-dimensional Matlab-based GPU-accelerated integrators using compact high-order schemes

Computer Physics Communications ◽

10.1016/j.cpc.2012.12.010 ◽

2013 ◽

Vol 184 (4) ◽

pp. 1250-1271 ◽

Cited By ~ 12

Author(s):

R.M. Caplan

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

High Order ◽

Nonlinear Schrödinger ◽

High Order Schemes

New Exact Envelope Traveling Wave Solutions of High-Order Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

Communications in Theoretical Physics ◽

10.1088/6102/44/5/799 ◽

2005 ◽

Vol 44 (5) ◽

pp. 799-801 ◽

Cited By ~ 20

Author(s):

Cheng-Shi Liu

Keyword(s):

Schrödinger Equation ◽

Traveling Wave ◽

Schrodinger Equation ◽

Traveling Wave Solutions ◽

Quintic Nonlinear Schrödinger Equation

High Order ◽

Nonlinear Schrödinger ◽

Wave Solutions ◽

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 ◽

Wave Operator ◽

Schrodinger Equation ◽

Fractional Nonlinear Schrödinger Equation

Conservative Scheme ◽

Nonlinear Schrödinger ◽

Diffraction induced high-order modes of the [2+1] nonparaxial nonlinear Schrodinger equation

International Quantum Electronics Conference, 2005. ◽

10.1109/iqec.2005.1561174 ◽

2005 ◽

Author(s):

S. Chavez-Cerda ◽

J.M. Hickmann

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

High Order ◽

Nonlinear Schrödinger

Exact solitary and periodic wave solutions of high-order nonlinear Schrödinger equation and their relationship with Hamilton energy

AIP Advances ◽

10.1063/5.0057688 ◽

2021 ◽

Vol 11 (8) ◽

pp. 085212

Author(s):

Weiguo Zhang ◽

Yuli Guo ◽

Siyu Hong ◽

Xingqian Ling

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Wave ◽

High Order ◽

Periodic Wave Solutions ◽

Nonlinear Schrödinger ◽

Hamilton Energy ◽

Wave Solutions

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 ◽

Schrodinger Equation ◽

High Order ◽

Exponential Integrators ◽

Structure Preserving ◽

Nonlinear Schrödinger