The Conservative and Efficient Numerical Method of 2-D and 3-D Fractional Nonlinear Schrödinger Equation Using Fast Cosine Transform

Author:

Wang Peiyao1,Peng Shangwen1,Cao Yihao1,Zhang Rongpei1

Affiliation:

1. School of Advanced Manufacturing, Guangdong University of Technology, Jieyang 522000, China

Abstract

This paper introduces a novel approach employing the fast cosine transform to tackle the 2-D and 3-D fractional nonlinear Schrödinger equation (fNLSE). The fractional Laplace operator under homogeneous Neumann boundary conditions is first defined through spectral decomposition. The difference matrix Laplace operator is developed by the second-order central finite difference method. Then, we diagonalize the difference matrix based on the properties of Kronecker products. The time discretization employs the Crank–Nicolson method. The conservation of mass and energy is proved for the fully discrete scheme. The advantage of this method is the implementation of the Fast Discrete Cosine Transform (FDCT), which significantly improves computational efficiency. Finally, the accuracy and effectiveness of the method are verified through two-dimensional and three-dimensional numerical experiments, solitons in different dimensions are simulated, and the influence of fractional order on soliton evolution is obtained; that is, the smaller the alpha, the lower the soliton evolution.

Publisher

MDPI AG

Reference32 articles.

1. Numerical approaches for solving the nonlinear Schrödinger equation in the nonlinear fiber optics formalism;Pottiez;J. Opt.,2020

2. Detecting a logarithmic nonlinearity in the Schrödinger equation using Bose-Einstein condensates;Vowe;Phys. Rev. A,2020

3. Review of heavy-nucleus-acoustic nonlinear structures in cold degenerate plasmas;Sultana;Rev. Mod. Plasma Phys.,2022

4. General higher-order rogue waves in the space-shifted symmetric nonlocal nonlinear Schrödinger equation;Rao;Acta Phys. Sin.,2023

5. Study on the generation mechanism of bright and dark solitary waves and rogue wave for a fourth-order dispersive nonlinear Schrödinger equation;Li;Acta Phys. Sin.,2020

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3