| 欧阳成,石兰芳,汪维刚,莫嘉琪.非线性强迫扰动Klein-Gordon方程的 孤波渐近解法[J].数学年刊A辑,2017,38(1):043~52 |
| 非线性强迫扰动Klein-Gordon方程的 孤波渐近解法 |
| The Asymptotic Solving Method of Solitary Wave for the Nonlinear Forced Disturbed Klein-Gordon Equation |
| Received:April 02, 2015 Revised:December 15, 2015 |
| DOI：10.16205/j.cnki.cama.2017.0005 |
| 中文关键词: Solitary waves, Functional, Nonlinear |
| 英文关键词:Solitary waves, Functional, Nonlinear |
| 基金项目:本文受到国家自然科学基金(No.11202106),浙江省自然科学研究项目(No.LY13A010005)和江苏省
高校自然科学研究项目(No.13KJB170016)的资助. |
| Author Name | Affiliation | E-mail | | OUYANG Cheng | Faculty of Science, Huzhou University, Huzhou 313000, Zhejiang, China. | oyc@hutc.zj.cn | | SHI Lanfang | College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China. | shilf@163.com | | WANG Weigang | Department of Science and Technology, Tongcheng Teachers College, Tongcheng 231402, Anhui, China. | shilf@163.com | | MO Jiaqi | Department of Mathematics, Anhui Normal University, Wuhu 241003, Anhui, China. | wwg12345@126.com |
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| 中文摘要: |
| 研究了一类非线性强迫扰动Klein-Gordon方程.
首先利用双曲正切待定系数法求得了典型的方程孤波解. 然后利用泛函变分迭代原理得到了强迫扰动
Klein-Gordon方程的一个近似解, 并论述了解的一致有效性. 所得到的近似解是一个解析式, 它还可对近似解
进行解析运算, 而使用简单的模拟方法所得到的近似解是达不到这种效果的. |
| 英文摘要: |
| A class of nonlinear forced disturbed Klein-Gordon equation is considered.
Firstly, the solitary waves to typical equation is solved using the method of
undetermined coefficients for hyperbolic tangent functions. Then approximate solutions of
soliton to nonlinear forced disturbed equation are obtained using the functional variational
principle. Finally, the uniform validity for the approximate solutions is proved. And the
asymptotic solution has an analytic expression, so the authors can carry on analytic operation to it,
these can not be obtained by using the simple simulate method. |
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