Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1
Chinese Journal of Engineering Mathematics

Chinese Journal of Engineering Mathematics ›› 2019, Vol. 36 ›› Issue (2): 179-186.doi: 10.3969/j.issn.1005-3085.2019.02.005

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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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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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