Dark solitons, breathers, and rogue wave solutions of the coupled generalized nonlinear Schrödinger equations

Abstract

We construct dark-dark soliton, general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of a coupled generalized nonlinear Schrödinger (CGNLS) equation. While dark-dark solitons are captured in the defocusing regime of the CGNLS system, the other solutions, namely, GB, AB, MS, and RW, are identified in the focusing regime. We also analyze the structures of GB, AB, MS, and RW profiles with respect to the four-wave mixing parameter. We show that when we increase the value of the real part of the four-wave mixing parameter, the number of peaks in the breather profile increases and the width of each peak shrinks. Interestingly, the direction of this profile also changes due to this change. As far as the RW profile is concerned the width of the peak becomes very thin when we increase the value of this parameter. Further, we consider the RW solution as the starting point, derive AB, MS, and GB in the reverse direction, and show that the solutions obtained in both directions match each other. In the course of the reverse analysis we also demonstrate how to capture the RW solutions directly from AB and MS.

Rogue waves in a two-component Manakov system with variable coefficients and an external potential

“…Additional novel RW patterns produced by multi-component models have been reported in Refs. [28][29][30][31][32][33][34][35][36]. In particular, the following types of RG solutions have been obtained in the system of two coupled NLSEs with constant coefficients: Breathers and rational-breather solutions of multi-component NLSEs were presented in Ref.…”

Orthogonally polarized bright–dark pulse pair generation in mode-locked fiber laser with a large-angle tilted fiber grating

“…The dark pulses are less sensitive to noise and fiber losses than the bright ones and hence are promising for robust optical communication [4]. Since the dark soliton transmission was first theoretically proposed in 1973 [5], the dark soliton formation and propagation in single-mode fibers (SMFs) has been extensively investigated on both theory and experiment [6][7][8][9][10]. It has been theoretically shown that both bright and dark solitons are solutions of the nonlinear Schrödinger equation (NLSE) [11], and can be supported in a fiber transmission line with dispersion management [12].…”

Breather and rogue wave solutions for a nonlinear Schrödinger-type system in plasmas

“…Physically, breathers can arise from the effect of modulation instability, which is a characteristic feature of various nonlinear dispersive systems, associated with energy exchange of periodic perturbation on a continuous wave background [42][43][44][45]. Based on the Expressions (10) and (11), the breather solutions of System (3) on the nonzero continuous background can be derived.…”