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Lyapunov stability of singular planar systems related to dispersion-managed solitons in optical fiber
  • +2
  • Zaitao Liang,
  • Xin Li,
  • Shengjun Li,
  • Xuemeng Shan,
  • Feng Wang
Zaitao Liang
Anhui University of Science and Technology
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Xin Li
Anhui University of Science and Technology
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Shengjun Li
Hainan University
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Xuemeng Shan
Anhui University of Science and Technology
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Feng Wang
Changzhou University
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Abstract

In this paper, we consider two singular planar differential systems which can describe the evolution of the optical pulse width and chirp for the so-called dispersion-managed solitons. Based on the method of third order approximation in combination with some quantitative information obtained by the upper-lower solutions method and the averaging method, some results on the existence and Lyapunov stability of the periodic solutions are obtained. Moreover, the formula of the first twist coefficient and a stability criterion of a nonlinear differential equation are also established.

Peer review status:UNDER REVIEW

03 Apr 2021Submitted to Mathematical Methods in the Applied Sciences
05 Apr 2021Assigned to Editor
05 Apr 2021Submission Checks Completed
11 Apr 2021Reviewer(s) Assigned