A two-step high-order compact scheme for the Laplacian operator and its implementation in an explicit method for integrating the nonlinear Schrödinger equation

Schrodinger Equation ◽

High Order ◽

Compact Scheme ◽

Laplacian Operator ◽

Explicit Method ◽

Nonlinear Schrödinger ◽

High Order Compact Scheme

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 ◽

Wave Operator ◽

Schrodinger Equation ◽

Auxiliary Variable ◽

High Order ◽

Nonlinear Schrödinger ◽

Order Energy ◽

Variable Approach

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 ◽

Optimal error estimate of a compact scheme for nonlinear Schrödinger equation

Applied Numerical Mathematics ◽

10.1016/j.apnum.2017.05.004 ◽

2017 ◽

Vol 120 ◽

pp. 68-81 ◽

Cited By ~ 6

Author(s):

Jialin Hong ◽

Lihai Ji ◽

Linghua Kong ◽

Tingchun Wang

Keyword(s):

Schrödinger Equation ◽

Error Estimate ◽

Schrodinger Equation ◽

Compact Scheme ◽

Optimal Error Estimate ◽

Optimal Error ◽

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 ◽

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 ◽

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 ◽

High-order rational solutions and rogue wave for the (2 + 1)-dimensional nonlinear Schrödinger equation

Physica Scripta ◽

10.1088/1402-4896/ab4eb3 ◽

2020 ◽

Vol 95 (4) ◽

pp. 045204

Author(s):

Wenhao Liu ◽

Yufeng Zhang

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Rogue Wave ◽

High Order ◽

Rational Solutions ◽