loading page

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

Corresponding Author:ztliang@aust.edu.cn

Author Profile
Xin Li
Anhui University of Science and Technology
Author Profile
Shengjun Li
Hainan University
Author Profile
Xuemeng Shan
Anhui University of Science and Technology
Author Profile
Feng Wang
Changzhou University
Author Profile

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.