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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (2): 179-186.doi: 10.3969/j.issn.1005-3085.2019.02.005

• • 上一篇    下一篇

一类非线性广义强阻尼时滞扰动Sine-Gordon方程初值问题

冯依虎1,2,  汪维刚3,   莫嘉琪4   

  1. 1- 亳州学院电子与信息工程系，亳州  236800
    2- 上海大学数学系，上海  200436
    3- 合肥幼儿师范高等专科学校基础部，合肥   230011
    4- 安徽师范大学数学与统计学院，芜湖  241003
  • 收稿日期:2017-03-22 接受日期:2017-09-28 出版日期:2019-04-15 发布日期:2019-06-15
  • 基金资助:
    国家自然科学基金(11202106)；安徽省教育厅自然科学重点基金(KJ2017A702; KJ2017A704; KJ2017A901; KJ2018A0964)；安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016520)；亳州学院教学研究重点项目(2017zdjy02)；亳州学院自然科学研究重点项目(BYZ2017B02).

A Class of Nonlinear Generalized Strong Damping Time Delay Disturbed Sine-Gordon Equation Initial Value Problem

FENG Yi-hu1,2,   WANG Wei-gang3,   MO Jia-qi4   

  1. 1- Department of Electronics and Information Engineering, Bozhou College, Bozhou 236800
    2- Department of Mathematics, Shanghai University, Shanghai 200436
    3- Department of Basic, Hefei Preschool Education College, Hefei 230011
    4- School of Mathematics and Statistics, Anhui Normal University, Wuhu 241003
  • Received:2017-03-22 Accepted:2017-09-28 Online:2019-04-15 Published:2019-06-15
  • Supported by:
    The National Natural Science Foundation of China (11202106); the National Science Foundation of the Education Deoartment of Anhui Province (KJ2017A702; KJ2017A704; KJ2017A901; KJ2018A0964); the Key Projects of Outstanding Young Talents of Universities in Anhui Province (gxyqZD2016520); the Teaching and Research Key Project of Bozhou University (2017zdjy02); the Natural Science Key Project of Bozhou University (BYZ2017B02).

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摘要： 本文讨论了一类非线性广义Sine-Gordon扰动方程，基于渐近理论得到对应方程的时滞初值问题并求出渐近解析解．首先，利用Fourier变换方法得出外部解．其次，按时滞变量展开扰动函数，再根据摄动方法和理论求出强阻尼时滞扰动广义Sine-Gordon方程初值问题的的渐近解．根据本文的理论和方法得到的渐近解是解析的表示式，能够进行解析运算，从而可得到相关的物理量的性状，扩大了问题的讨论范围．

关键词: 非线性, 扰动, 强阻尼

Abstract: In this paper, a class of nonlinear generalized Sine-Gordon disturbed equation is considered. From the asymptotic theory, the asymptotic analytic solution to corresponding equation time delay initial value problem is solved. Firstly, the outer solution is found by using the Fourier transform method. Secondly, the disturbed function is developed from the time delay variable. Then, the uniformly valid solution to the strong damping time delay disturbed generalized Sine-Gordon equation initial value problem is obtained by the perturbation method and theory. Moreover, the asymptotic solution is an analytic expansion, and able to do analytic operation. Therefore, the corresponding physical characters are derived, and application fields are enlarged.

Key words: nonlinear, perturbation, strong damp

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