非线性高维扰动Klein-Gordon方程的孤子波摄动解

doi:10.3969/j.issn.1000-5641.2019.06.003

华东师范大学学报(自然科学版) ›› 2019, Vol. 2019 ›› Issue (6): 21-28.doi: 10.3969/j.issn.1000-5641.2019.06.003

非线性高维扰动Klein-Gordon方程的孤子波摄动解

徐建中¹, 莫嘉琪²

1. 亳州学院电子与信息工程系, 安徽亳州 236800;
2. 安徽师范大学数学与统计学院, 安徽芜湖 241003

收稿日期:2018-08-14 出版日期:2019-11-25 发布日期:2019-11-26
通讯作者: 莫嘉琪,男,教授,研究方向为应用数学、生态数学、数学物理、工程数学.E-mail:mojiaqi@mail.ahnu.edu.cn. E-mail:mojiaqi@mail.ahnu.edu.cn
作者简介:徐建中,男,副教授,研究方向为应用数学、生态数学.E-mail:xujianzhongok@163.com.
基金资助:
国家自然科学基金（41275062）；安徽省高校自然科学研究重点项目（KJ2017A704，KJ2019A1303）；安徽省高校优秀青年人才支持计划项目（gxyq2018116）；安徽省优秀教学团队基金（2016jytd080）；亳州学院自然科学研究重点项目（BYZ2018B03）

Perturbation solution for a solitary wave of the nonlinear higher dimensional disturbed Klein-Gordon equation

XU Jian-zhong¹, MO Jia-qi²

1. Department of Electronics and Information Engineering, Bozhou University, Bozhou Anhui 236800, China;
2. School of Mathematics and Statistics, Anhui Normal University, Wuhu Anhui 241003, China

Received:2018-08-14 Online:2019-11-25 Published:2019-11-26

摘要/Abstract

摘要： 利用广义变分迭代方法讨论了一类非线性强迫扰动Klein-Gordon方程.首先，用双曲函数待定系数法求得了无扰动方程孤子波.其次，利用泛函变分迭代原理得到了强迫扰动Klein-Gordon方程的一个摄动近似解.最后，论述了解的一致有效性.得到的近似解是解析式，它可对近似解进行解析运算，这对用简单的模拟方法得到的近似解是达不到的.

关键词: 摄动解, 孤子波, 变分迭代

Abstract: In this paper, a class of nonlinear forced disturbed Klein-Gordon equations are considered using the method of generalized variational iteration. Firstly, the solitary waves of an undisturbed Klein-Gordon equation are solved using the method of undetermined coefficients for hyperbolic functions. Then, perturbed approximate solutions for a soliton of a nonlinear forced disturbed Klein-Gordon equation are obtained using the functional variational iterative principle. Finally, the uniform validity for the approximate solutions is proved. The obtained approximate solution is an analytic expression. So it can be used for carrying out analytic operations. However, these cannot be obtained via a simple simulation.

Key words: perturbation solution, solitary waves, variational iteration

中图分类号:

O157.29

徐建中, 莫嘉琪. 非线性高维扰动Klein-Gordon方程的孤子波摄动解[J]. 华东师范大学学报(自然科学版), 2019, 2019(6): 21-28.

XU Jian-zhong, MO Jia-qi. Perturbation solution for a solitary wave of the nonlinear higher dimensional disturbed Klein-Gordon equation[J]. Journal of East China Normal University(Natural Sc, 2019, 2019(6): 21-28.

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非线性高维扰动Klein-Gordon方程的孤子波摄动解

Perturbation solution for a solitary wave of the nonlinear higher dimensional disturbed Klein-Gordon equation

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