Lax pair, Darboux transformation, breathers and rogue waves of an N-coupled nonautonomous nonlinear Schrödinger system for an optical fiber or a plasma

• Published in: Nonlinear dynamics 2022-02, Vol.107 (3), p.2657-2666
• Main Authors: Yang, Dan-Yu, Tian, Bo, Wang, Meng, Zhao, Xin, Shan, Wen-Rui, Jiang, Yan
• Format: Article
• Language: English
• Subjects: Amplitudes; Asymptotic properties; Automotive Engineering; Breathers; Chemical sensors; Classical Mechanics; Control; Dynamical Systems; Engineering; Integers; Investigations; Mechanical Engineering; Optical communication; Optical fibers; Original Paper; Plasma; Propagation; Sensors; Solitary waves; Vibration; Wave propagation
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-06886-2

Optical fibers are used in communication, biological sensors and chemical sensors. Plasma is considered to be the most abundant common form of matter in the Universe, supporting some phenomena. Considering the inhomogeneous effects, we have investigated an N -coupled nonautonomous nonlinear Schrödinger system, where N is a positive integer. With respect to the simultaneous wave propagation of N fields in an optical fiber or a plasma, we construct a Lax pair and n -fold Darboux transformation, with which we obtain the first- and second-order breather, and rogue wave solutions, where n is a positive integer. Amplitudes of the two solitons change after their interaction, while velocities of the two solitons are unchanged after their interaction via the asymptotic analysis. Characteristics of the breathers are presented. Interactions between the two breathers, and interactions between the first-order rogue waves and breather-like solitons are discussed. We find that the inhomogeneous coefficients in the system under investigation affect the backgrounds, amplitudes and trajectories of the breathers and rogue waves.