[1]郭钰卓,孙建强*,孔嘉萌.多辛sine-Gordon方程高阶保能量格式[J].江西师范大学学报(自然科学版),2019,(04):343-347.[doi:10.16357/j.cnki.issn1000-5862.2019.04.03]
 GUO Yuzhuo,SUN Jianqiang*,KONG Jiameng.The High Order Energy-Preserving Scheme of Multi-Symplectic sine-Gordon Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2019,(04):343-347.[doi:10.16357/j.cnki.issn1000-5862.2019.04.03]
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多辛sine-Gordon方程高阶保能量格式()
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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:
2019年04期
页码:
343-347
栏目:
数学与应用数学
出版日期:
2019-08-10

文章信息/Info

Title:
The High Order Energy-Preserving Scheme of Multi-Symplectic sine-Gordon Equation
文章编号:
1000-5862(2019)04-0343-05
作者:
郭钰卓孙建强*孔嘉萌
海南大学理学院,海南 海口 570228
Author(s):
GUO YuzhuoSUN Jianqiang*KONG Jiameng
School of Science,Hainan University,Haikou Hainan 570228,China
关键词:
多辛高阶保能量方法 平均向量场方法 Boole离散线积分法 sine-Gordon方程
Keywords:
multi-symplectic high order energy-preserving method average vector field method Boole discrete line integral method sine-Gordon equation
分类号:
O 241.5
DOI:
10.16357/j.cnki.issn1000-5862.2019.04.03
文献标志码:
A
摘要:
1维sine-Gordon方程通过适当的变换转化成相应多辛Hamilton偏微分方程,其中与时间变量偏导数有关的矩阵是可逆的,利用Hamilton系统的4阶平均向量场方法和Boole离散线积分方法得到了多辛sine-Gordon方程的一个新的4阶整体保能量格式.利用新格式数值模拟sine-Gordon方程.数值结果表明:新格式能较好地模拟sine-Gordon方程在不同初值条件下孤立波的运动,且保持了孤立波的能量守恒特性.
Abstract:
One dimension sine-Gordon equation is transformed into the multi-symplectic Hamiltonian partial differential equation through appropriate transformation,where the matrix with the time variable partial derivation is inverse.A new fourth-order energy-preserving scheme of multi-symplectic sine-Gordon equation is obtained by the fourth order average vector field method of the Hamiltonian system and the Boole discrete line integral method.The new scheme is applied to simulate sine-Gordon equation.Numerical results show that the new scheme can well simulate the solitary wave behaviors of sine-Gordon equation with different initial conditions,moreover preserve the energy conservation property of the solitary waves.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2019-03-28
基金项目:国家自然科学基金(11561018)资助项目.
通信作者:孙建强(1971-),男,湖南双峰县人,教授,博士,主要从事微分方程的数值解法的研究.E-mail:sunjq123@qq.com
更新日期/Last Update: 2019-08-10