高维弱扰动破裂孤子波方程行波解

张良; 林万涛; 陈贤峰; 莫嘉琪

doi:10.3879/j.issn.1000-0887.2015.11.008

高维弱扰动破裂孤子波方程行波解

doi: 10.3879/j.issn.1000-0887.2015.11.008

¹亳州师范高等专科学校电子与信息工程系, 安徽亳州 236800;²大气科学和地球流体力学数值模拟国家重点实验室(中国科学院大气物理研究所), 北京 100029;³上海交通大学数学系, 上海 200240;⁴安徽师范大学数学系, 安徽芜湖 241003

基金项目: 国家自然科学基金(41275062;11371248);安徽省教育厅自然科学课题(KJ2015A347;KJ2013B153)

详细信息

作者简介:
张良(1962—)，男, 安徽蒙城人, 副教授, 硕士(E-mail: bzszzhangl@163.com);莫嘉琪(1937—)，男，浙江德清人，教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

中图分类号: O175.29
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出版历程
- 收稿日期: 2015-06-15
- 修回日期: 2015-07-10
- 刊出日期: 2015-11-15

Travelling Solutions to High-Dimensional Weakly Perturbed Breaking Soliton Wave Equations

¹Department of Electronics and Information Engineering, Bozhou Teachers College, Bozhou, Anhui 236800, P.R.China;²State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(Institute of Atmospheric Physics, Chinese Academy of Sciences), Beijing 100029, P.R.China;³Department of Mathematics,Shanghai Jiao Tong University, Shanghai 200240, P.R.China;⁴Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(41275062;11371248)

摘要

摘要: 研究了一类高维弱扰动破裂孤子波方程.首先讨论了对应的典型破裂孤子波方程, 利用待定系数投射方法得到了孤子波精确解.再利用泛函分析和摄动理论得到了原弱扰动破裂孤子波方程的孤子行波渐近解.最后, 举出例子说明了用该方法得到的弱扰动破裂孤子波方程的行波渐近解具有简捷、有效和较高精度的优点.
- Korteweg-de Vries方程 /
- 弱扰动 /
- 渐近解
Abstract: A class of high-dimensional weakly perturbed breaking solitary wave equations were studied. Firstly, the corresponding typical breaking solitary wave equations were considered. The exact solitary wave solution was obtained with the throwing method of undetermined coefficients. Then, the travelling wave asymptotic solution to the original weakly perturbed breaking solitary wave equation was found through functional analysis based on the perturbation theories. Finally, with an example, the proposed travelling wave asymptotic solution to the weakly perturbed breaking solitary wave equation shows the merits of simpleness, validity and good accuracy.
- Korteweg-de Vries equation /
- weak perturbation /
- asymptotic solution

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参考文献(17)

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文章访问数: 1255
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高维弱扰动破裂孤子波方程行波解

doi: 10.3879/j.issn.1000-0887.2015.11.008

作者简介:
张良(1962—)，男, 安徽蒙城人, 副教授, 硕士(E-mail: bzszzhangl@163.com);莫嘉琪(1937—)，男，浙江德清人，教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

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Travelling Solutions to High-Dimensional Weakly Perturbed Breaking Soliton Wave Equations

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留言板

高维弱扰动破裂孤子波方程行波解

doi: 10.3879/j.issn.1000-0887.2015.11.008

作者简介: 张良(1962—)，男, 安徽蒙城人, 副教授, 硕士(E-mail: bzszzhangl@163.com);莫嘉琪(1937—)，男，浙江德清人，教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

计量

出版历程

Travelling Solutions to High-Dimensional Weakly Perturbed Breaking Soliton Wave Equations

计量

出版历程

目录

作者简介:
张良(1962—)，男, 安徽蒙城人, 副教授, 硕士(E-mail: bzszzhangl@163.com);莫嘉琪(1937—)，男，浙江德清人，教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).