[1]张利娟,孙建强*.分数阶Klein-Gordon-Schrdinger方程的保能量方法[J].江西师范大学学报(自然科学版),2022,(03):257-261.[doi:10.16357/j.cnki.issn1000-5862.2022.03.07]
　ZHANG Lijuan,SUN Jianqiang.The Energy-Preserving Method for the Fractional Klein-Gordon-Schrdinger Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2022,(03):257-261.[doi:10.16357/j.cnki.issn1000-5862.2022.03.07]
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分数阶Klein-Gordon-Schrödinger方程的保能量方法()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2022年03期
页码:
257-261
栏目:
数学与应用数学
出版日期:
2022-05-25

文章信息/Info

Title:
The Energy-Preserving Method for the Fractional Klein-Gordon-Schrödinger Equation
文章编号:
1000-5862(2022)03-0257-05
作者:
张利娟; 孙建强*
海南大学理学院,海南 海口 570228
Author(s):
ZHANG Lijuan; SUN Jianqiang
College of Science,Hainan University,Haikou Hainan 570228,China
关键词:
平均向量场方法;  分数阶Klein-Gordon-Schrö; dinger方程;  傅里叶拟谱方法;  能量守恒格式
Keywords:
average vector field method;  fractional Klein-Gordon-Schrö; dinger equation;  Fourier pseudo-pectral method;  the scheme of conservation of energy
分类号:
O 241.5
DOI:
10.16357/j.cnki.issn1000-5862.2022.03.07
文献标志码:
A
摘要:
该文先将分数阶Klein-Gordon-Schrödinger方程转化成辛结构的哈密尔顿系统,利用傅里叶拟谱方法对Riesz空间分数阶导数进行近似离散,得到分数阶Klein-Gordon-Schrödinger方程有限维哈密尔顿系统; 再利用2阶平均向量场方法对有限维哈密尔顿系统离散,得到分数阶Klein-Gordon-Schrödinger方程新的保能量格式; 最后利用新的保能量格式数值模拟方程孤立波的演化行为,并分析新格式的保能量守恒特性.
Abstract:
The fractional Klein-Gordon-Schrödinger equation are transformed into the Hamiltonian system with the symplectic structure.The Riesz space-fractional derivation is discretized approximately by the Fourier pseudo-pectral method.The finite dimensional Hamiltonian system of the fractional Klein-Gordon-Schrödinger equation is obtained.The second order average vector field method is applied to solve the finite dimensional Hamiltonian system.The new energy preserving scheme of the fractional Klein-Gordon-Schrödinger equation is obtained.The new scheme is applied to numerically simulate the solitary evolution behaviors of the equation,moreover the energy conservation property of the new scheme is investigated.

参考文献/References:

[1] UCHAIKIN V V.Fractional derivatives for physicists and engineers[M].Beijing:Higher Education Press,2013:230-240.
[2] TARASOV V.Fractional dynamics:applications of fractional calculus to dynamics of particles,fields and media[M].Beijing:Higher Education Press,2011:163-180.
[3] LI Changpin,ZENG Fanhai.Numerical methods for fractional calculus[M].New York:CRC Press,2015:1-17.
[4] DING Hengfei,LI Changpin.High-order numerical algorithms for Riesz derivatives via constructing new generating functions[J].Journal of Scientific Computing,2017,71(2):759-784.
[5] RAN Maohua,ZHANG Chengjian.A conservative difference scheme for solving the strongly coupled nonlinear fractional Schrödinger equations[J].Communications in Nonlinear Science and Numerical Simulation,2016,41:64-83.
[6] 刘发旺,庄平辉,刘青霞.分数阶偏微分方程数值方法及其应用[M].北京:科学出版社,2015:320-340.
[7] WANG Junjie,XIAO Aiguo.A efficient conservation difference scheme for fractional Klein-Gordon-Schrödinger equations[J].Applied Mathematics and Computation,2018,320:691-709.
[8] OHTA M.Stability of stationary states for coupled Klein-Gordon-Schrödinger equations[J].Nonlinear Analysis:Theory,Methods & Applications,1996,27(4):455-461.
[9] KONG Linghua,CHEN Meng,YIN Xiuling.A novel kind of efficient symplectic scheme for Klein-Gordon-Schrödinger equation[J].Applied Numerical Mathematics,2019,135:481-496.
[10] HUANG Chunyan,GUO Boling,HUANG Daiwen,et al.Global well-posedness of the fractional Klein-Gordon-Schrödinger system with rough initial data[J].Science China:Mathematics,2016,59(7):1345-1366.
[11] WANG Junjie,XIAO Aiguo.Conservative fourier spectral method and numericalinvestigation of space fractional Klein-Gordon-Schrödinger equations[J].Applied Mathematics and Computation,2019,350:348-365.
[12] QUISPEL G R W,MCLAREN D I.A new class of energy-preserving numerical integration methods[J].Journal of Physics A:Mathematical and Theoretical,2008,41(4):045206.
[13]CELLEDONI E,MCLACHLAN R I,OWREN B,et al.On conjugate B-series and their geometric structure[J].Journal of Numerical Analysis,Industrial and Applied Mathematics,2010,5(1/2):85-94.
[14] MCLACHLAN R I,QUISPEL G R W,ROBIDOUX N.Geometric integration using discrete gradients[J].Philosophical Transactions of the Royal Society B Biological Sciences,1999,357(1754):1021-1045.
[15] 李昊辰,孙建强,骆思宇.非线性薛定谔方程的平均向量场方法[J].计算数学学报,2013,35(1):59-66.
[16] JIANG Chaolong,SUN Jianqiang,LI Haochen,et al.A fourth-order AVF method for the numerical integration of sine-Gordon equation[J].Applied Mathematics and Computation,2017,313:144-158.
[17] RAY S S.A new analytical modelling for nonlocal generalized Riesz fractional sine-Gordon equation[J].Journal of King Saud University:Science,2016,28(1):48-54.
[18] WANG Pengde,HUANG Chengming.Structure-preserving numerical methods for the fractional Schrödinger equation[J].Applied Numerical Mathematics,2018,129:137-158.
[19] CHEN Jingbo.Symplectic and multisymplectic Fourierpseudospectral discretizations for the Klein-Gordon equation[J].Letters in Mathematical Physics,2006,75(3):293-305.

相似文献/References:

[1]闫静叶,孙建强.复修正KdV方程的高阶保能量方法[J].江西师范大学学报(自然科学版),2016,40(02):209.
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备注/Memo

备注/Memo:
收稿日期:2021-10-15
基金项目:国家自然科学基金(11961020)资助项目。
通信作者:孙建强(1971—),男,湖南双峰人,教授,博士,主要从事微分方程的数值解法研究.E-mail:sunjq123@qq.com
更新日期/Last Update: 2022-05-25