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非线性高维扰动Klein-Gordon方程的孤子波摄动解

徐建中 莫嘉琪

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, (6): 21-28. doi: 10.3969/j.issn.1000-5641.2019.06.003
引用本文: 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, (6): 21-28. doi: 10.3969/j.issn.1000-5641.2019.06.003
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 Sciences), 2019, (6): 21-28. doi: 10.3969/j.issn.1000-5641.2019.06.003
Citation: 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 Sciences), 2019, (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

doi: 10.3969/j.issn.1000-5641.2019.06.003
基金项目: 

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

安徽省高校自然科学研究重点项目 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

详细信息
    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

    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

  • 中图分类号: O157.29

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

  • 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.
  • 图  1  非线性方程(4)的孤子波曲线(11)

    Fig.  1  The solitary waves curve (11) of nonlinear equation (4)

    图  2  非线性KG方程(22)的孤子波扰动解的曲线

    Fig.  2  The curve of solitary waves disturbed solutions to the nonlinear KG equation (22)

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出版历程
  • 收稿日期:  2018-08-14
  • 刊出日期:  2019-11-25

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