[1]郭姣姣,庄清渠.求解耦合非线性Schr?dinger-Boussinesq方程的三角标量辅助变量方法[J].华侨大学学报(自然科学版),2024,45(1):98-107.[doi:10.11830/ISSN.1000-5013.202306027]
　GUO Jiaojiao,ZHUANG Qingqu.Trigonometric Scalar Auxiliary Variable Method for Coupled Nonlinear Schr?dinger-Boussinesq Equation[J].Journal of Huaqiao University(Natural Science),2024,45(1):98-107.[doi:10.11830/ISSN.1000-5013.202306027]
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求解耦合非线性Schr?dinger-Boussinesq方程的三角标量辅助变量方法()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第45卷
期数:
2024年第1期
页码:
98-107
栏目:
出版日期:
2024-01-11

文章信息/Info

Title:
Trigonometric Scalar Auxiliary Variable Method for Coupled Nonlinear Schr?dinger-Boussinesq Equation
文章编号:
1000-5013(2024)01-0098-10
作者:
郭姣姣;  庄清渠
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
GUO Jiaojiao;  ZHUANG Qingqu
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
耦合非线性Schr? dinger-Boussinesq方程;  三角标量辅助变量方法;  修正能量;  守恒律
Keywords:
coupled nonlinear Schr? dinger-Boussinesq equation;  trigonometric scalar auxiliary variable method;  modified energy;  conservation law
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.202306027
文献标志码:
A
摘要:
采用三角标量辅助变量(TSAV)方法,构造求解耦合非线性Schr?dinger-Boussinesq方程初边值问题的高效数值格式。基于方程非线性势能的三角函数形式,提出求解方程的TSAV格式;对方程在时间和空间上分别采用二阶Crank-Nicolson格式和傅里叶谱方法进行离散,并证明时间半离散格式的修正能量守恒律。最后,通过数值算例对文中格式进行验证。结果表明:文中格式具有有效性,修正能量具有守恒性。
Abstract:
Based on the trigonometric scalar auxiliary variable(TSAV)method, an efficient numerical scheme is constructed to solve the initial boundary value problem of the coupled nonlinear Schr?dinger-Boussinesq equation. Firstly, based on the trigonometric function form of the nonlinear potential energy equation, the TSAV scheme of the considered equation is proposed. Then, the equation is discretized in temporal and spatial by using the second-order Crank-Nicolson scheme and Fourier spectral method respectively, and the modified energy conservation law of time semi-discrete scheme is proved. Finally, the proposed scheme is verified by numerical examples. The results show that the proposed scheme is effective and the modified energy is conserved.

参考文献/References:

[1] CHAE D.Global regularity for the 2D Boussinesq equations with partial viscosity terms[J].Advances in Mathematics,2006,203(2):497-513.DOI:10.1016/j.aim.2005.05.001.
[2] 孙传志,汪佳玲.非线性薛定谔方程的几种差分格式[J].华侨大学学报(自然科学版),2021,42(4):551-560.DOI:10.11830/ISSN.1000-5013.202011019.
[3] MAKHANKOV V G.On stationary solutions of the Schr?dinger equation with a self-consistent potential satisfying Boussinesq’s equation[J].Physics Letters A,1974,50(1):42-44.DOI:10.1016/0375-9601(74)90344-2.
[4] GUO Boling,DU Xianyun.Existence of the periodic solution for the weakly damped Schr?dinger-Boussinesq equation[J].Journal of Mathematical Analysis and Applications,2001,262(2):453-472.DOI:10.1006/jmaa.2000.7455.
[5] FARAH L G,PASTOR A.On the periodic Schr?dinger-Boussinesq system[J].Journal of Mathematical Analysis and Applications,2010,368(1):330-349.DOI:10.1016/j.jmaa.2010.03.007.
[6] YANG Yining,SUN Ziyu,LIU Yang,et al.Structure-preserving BDF2 FE method for the coupled Schr?dinger-Boussinesq equations[J].Numerical Algorithms,2023,93(3):1243-1267.DOI:10.1007/s11075-022-01466-w.
[7] TIAN Jiale,SUN Ziyu,LIU Yang,et al.TT-M finite element algorithm for the coupled Schr?dinger-Boussinesq equations[J].Axioms,2022,11(7):314.DOI:10.3390/axioms11070314.
[8] ORUC O.A local radial basis function-finite difference(RBF-FD)method for solving 1D and 2D coupled Schr?dinger-Boussinesq(SBq)equations[J].Engineering Analysis with Boundary Elements,2021,129:55-66.DOI:10.1016/j.enganabound.2021.04.019.
[9] CAI Jiaxiang,YANG Bin,ZHANG Chun.Efficient mass-and energy-preserving schemes for the coupled nonlinear Schr?dinger-Boussinesq system[J].Applied Mathematics Letters,2019,91:76-82.DOI:10.1016/j.aml.2018.11.024.
[10] DENG Dingwen,WU Qiang.Analysis of the linearly energy-and mass-preserving finite difference methods for the coupled Schr?dinger-Boussinesq equations[J].Applied Numerical Mathematics,2021,170:14-38.DOI:10.1016/j.apnum.2021.07.013.
[11] DENG Dingwen,WU Qiang.Linearized and decoupled structure-preserving finite difference methods and their analyses for the coupled Schr?dinger-Boussinesq equations[J].Numerical Methods for Partial Differential Equations,2021,37(5):2924-2951.DOI:10.1002/num.22805.
[12] LIAO Feng,ZHANG Luming,WANG Tingchun.Two energy-conserving and compact finite difference schemes for two-dimensional Schr?dinger-Boussinesq equations[J].Numerical Algorithms,2020,85:1335-1363.DOI:10.1007/s11075-019-00867-8.
[13] LIAO Feng,ZHANG Luming.Numerical analysis of a conservative linear compact difference scheme for the coupled Schr?dinger-Boussinesq equations[J].International Journal of Computer Mathematics,2018,95(5):961-978.DOI:10.1080/00207160.2017.1302082.
[14] BAI Dongmei,ZHANG Luming.The quadratic B-spline finite-element method for the coupled Schr?dinger-Boussinesq equations[J].International Journal of Computer Mathematics,2011,88(8):1714-1729.DOI:10.1080/00207160.2010.522234.
[15] LIAO Feng,ZHANG Luming,WANG Shanshan.Time-splitting combined with exponential wave integrator Fourier pseudospectral method for Schr?dinger-Boussinesq system[J].Communications in Nonlinear Science and Numerical Simulation,2018,55:93-104.DOI:10.1016/j.cnsns.2017.06.033.
[16] HE Yuyu,CHEN Hongtao.Efficient and conservative compact difference scheme for the coupled Schr?dinger-Boussinesq equations[J].Applied Numerical Mathematics,2022,182:285-307.DOI:10.1016/j.apnum.2022.08.013.
[17] SHEN Jie,XU Jie,YANG Jiang.The scalar auxiliary variable(SAV)approach for gradient flows[J].Journal of Computational Physics,2018,353:407-416.DOI:10.1016/j.jcp.2017.10.021.
[18] 郭姣姣,庄清渠.求解耦合非线性Klein-Gordon-Schr?dinger方程的能量稳定方法[J].华侨大学学报(自然科学版),2023,44(4):533-540.DOI:10.11830/ISSN.1000-5013.202206030.
[19] YANG Junxiang,KIM J.The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes[J].Journal of Engineering Mathematics,2021,129(1):18.DOI:10.1007/s10665-021-10155-x.
[20] TIAN Zhihui,RAN Maohua,LIU Yang.Higher-order energy-preserving difference scheme for the fourth-order nonlinear strain wave equation[J].Computers Mathematics with Applications,2023,135:124-133.DOI:10.1016/j.camwa.2023.01.026.
[21] ZHANG Xi,RAN Maohua,LIU Yang,et al.A high-order structure-preserving difference scheme for generalized fractional Schr?dinger equation with wave operator[J].Mathematics and Computers in Simulation,2023,210:532-546.DOI:10.1016/j.matcom.2023.03.027.

备注/Memo

备注/Memo:
收稿日期: 2023-06-29
通信作者: 庄清渠(1980-),男,副教授,博士,主要从事微分方程数值解法的研究。E-mail:qqzhuang@hqu.edu.cn。
基金项目: 国家自然科学基金资助项目(11771083); 福建省自然科学基金资助项目(2021J01306)
更新日期/Last Update: 2024-01-20