Contents lists available at ScienceDirect Optik journal homepage: www.elsevier.com/locate/ijleo Original research article Dark soliton control based on dispersion and nonlinearity for third- order nonlinear Schrödinger equation Chenjian Wang a , Zizhuo Nie b , Weijie Xie a , Jingyi Gao a , Qin Zhou c, ⁎ , Wenjun Liu a, ⁎ a State Key Laboratory of Information Photonics and Optical Communications, and School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, PR China b School of Physics and Optoelectronic Engineering Xidian University, Xi’an 710071, PR China c School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, PR China ARTICLE INFO Keywords: Solitons Analytic solution Dark solitons Soliton control ABSTRACT Nonlinear control is widely used in optical communications, ultrafast optics and other fields. In this paper, nonlinear control based on the dark soliton is investigated in the dispersion man- agement system. Dark soliton solutions for the third-order nonlinear Schrödinger equation are derived. Through changing the group velocity dispersion and nonlinear parameters, the propa- gation characteristics of dark solitons are discussed, and the influences of corresponding para- meters on dark solitons are analyzed. Some nonlinear control methods based on specific para- meters are suggested. Results are beneficial to the study of the dark soliton transmission. 1. Introduction As society enters the information age, the explosive growth of information has put tremendous pressure on the backbone. In order to alleviate the transmission pressure caused by a large amount of information, and to meet the demand for information in modern society, optical fiber technology emerges as the time requires, and develops toward high speed and high carrying capacity [1–6]. However, dispersion and nonlinear effects occur inevitably in the transmission process, which cause some difficulty in increasing the transmission rate of the optical fiber. When the dispersion and nonlinear effects reach equilibrium, transmitted optical pulses can form solitons effectively. Therefore, theoretical and experimental researches on solitons have been widely carried out [7–21]. In the application of solitons, how to control the balance between dispersion and nonlinear effects becomes an important problem in ultrafast optics [22–45]. The mathematical model of soliton transmission in the optical fiber has been studied in some literatures [46–51]. The generalized nonlinear Schrödinger (NLS) equation to model the soliton transmission in the inhomogeneous optical fiber has been investigated analytically [46]. The soliton transmission characteristics for analytic three-soliton solutions have been analyzed [47]. Through choosing the different parameters, soliton interactions have been discussed to the application of optical switching [48]. In this paper, when the pulse duration is less than 1 ps, the Raman gain effect should be taken into account. In this case, we consider a variable-coefficient third-order NLS equation with the following form [1], ∂ ∂ − ⎡ ⎣ ⎢ ∂ ∂ − ⎤ ⎦ ⎥ + ⎡ ⎣ ⎢ ∂ ∂ − ⎤ ⎦ ⎥ = i qxt x α x qxt t qxt qxt iα x qxt t qxt qxt (, ) () (, ) 2|(, )| (, ) () (, ) 6|(, )| (, ) 0, 2 2 2 2 3 3 3 2 (1) https://doi.org/10.1016/j.ijleo.2019.04.020 Received 2 April 2019; Accepted 2 April 2019 ⁎ Corresponding authors. E-mail addresses: qinzhou@whu.edu.cn (Q. Zhou), jungliu@bupt.edu.cn (W. Liu). Optik - International Journal for Light and Electron Optics 184 (2019) 370–376 0030-4026/ © 2019 Elsevier GmbH. All rights reserved. T