Evolution of periodic wave and dromion-like structure solutions in the variable coefficients coupled high-order complex Ginzburg–Landau system

• Published in: Nonlinear dynamics 2023-09, Vol.111 (18), p.17463-17471
• Main Authors: Yan, Yuanyuan, Liu, Wenjun, Wang, Haotian, Liu, Xiaoyan, Meng, Xiankui, Yang, Hujiang, Tian, Ye
• Format: Article
• Language: English
• Subjects: Asymmetry; Automotive Engineering; Classical Mechanics; Coefficients; Communications systems; Control; Dynamic characteristics; Dynamical Systems; Engineering; Evolution; Fiber lasers; Landau-Ginzburg equations; Mathematical analysis; Mechanical Engineering; Optical communication; Optimization; Original Paper; Solitary waves; Vibration; Wave division multiplexing; Wavelength division multiplexing
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-023-08742-x

In this paper, the propagation characteristics of ultrashort pulses in the birefringent fiber expressed by the variable coefficients coupled high-order complex Ginzburg–Landau equations (HCGLEs) are analyzed. Firstly, the one-soliton solution of the coupled HCGLEs is obtained by the asymmetric method. And this is an innovative breakthrough in applying the asymmetric method to solve the coupled Ginzburg–Landau (GL) equations for the first time. Then, the evolution process and dynamic characteristics of special types of solitons such as the periodic wave and dromion-like structure in the variable coefficients coupled high-order complex Ginzburg–Landau (HCGL) system are discussed by examples. Furthermore, the combination of traditional bright soliton and dromion-like structure is constructed for the first time. These works are expected to promote the research on multi-soliton solutions in HCGL systems, which is still an unsolved problem, and are likely to contribute some theoretical guidance to the optimization of wavelength division multiplexing (WDM) systems and the preparation of special types of soliton pairs in fiber lasers, so as to promote the development of optical soliton research and elevate information transmission rate in optical communication systems.