scholarly journals Modulation Instability, Breathers, and Bound Solitons in an Erbium-Doped Fiber System with Higher-Order Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Rui Guo ◽  
Hui-Qin Hao ◽  
Xiao-Song Gu
Keyword(s):  
Darboux Transformation ◽  
Modulation Instability ◽  
Lax Pair ◽  
Optical Solitons ◽  
Higher Order ◽  
Order Effects ◽  
Fiber System ◽  
Erbium Doped ◽  
Propagation Properties ◽  
Higher Order Effects

We mainly investigate the generalized nonlinear Schrödinger-Maxwell-Bloch system which governs the propagation of optical solitons in nonlinear erbium-doped fibers with higher-order effects. We deduce Lax pair, analyze modulation instability conditions, construct the Darboux transformation, and derive the Akhmediev breathers, Ma-breathers, bound solitons, and two-breather solutions for this system. Considering the influences of higher-order effects, propagation properties of those solitons are discussed.

scholarly journals Superregular breathers, characteristics of nonlinear stage of modulation instability induced by higher-order effects

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160681 ◽  
Author(s):  
Jian-Hui Zhang ◽  
Lei Wang ◽  
Chong Liu
Keyword(s):  
Darboux Transformation ◽  
Optical Pulse ◽  
Modulation Instability ◽  
Higher Order ◽  
Order Effects ◽  
Optical Fibres ◽  
Ultrashort Optical Pulse ◽  
Nls Equation ◽  
Nonlinear Stage ◽  
Higher Order Effects

We study the higher-order generalized nonlinear Schrödinger (NLS) equation describing the propagation of ultrashort optical pulse in optical fibres. By using Darboux transformation, we derive the superregular breather solution that develops from a small localized perturbation. This type of solution can be used to characterize the nonlinear stage of the modulation instability (MI) of the condensate. In particular, we show some novel characteristics of the nonlinear stage of MI arising from higher-order effects: (i) coexistence of a quasi-Akhmediev breather and a multipeak soliton; (ii) two multipeak solitons propagation in opposite directions; (iii) a beating pattern followed by two multipeak solitons in the same direction. It is found that these patterns generated from a small localized perturbation do not have the analogues in the standard NLS equation. Our results enrich Zakharov’s theory of superregular breathers and could provide helpful insight on the nonlinear stage of MI in presence of the higher-order effects.

scholarly journals Rogue waves in a resonant erbium-doped fiber system with higher-order effects

2016 ◽  
Vol 273 ◽  
pp. 826-841 ◽  
Author(s):  
Yu Zhang ◽  
Chuanzhong Li ◽  
Jingsong He
Keyword(s):  
Rogue Waves ◽  
Higher Order ◽  
Order Effects ◽  
Fiber System ◽  
Erbium Doped ◽  
Higher Order Effects

scholarly journals Characteristics of optical multi-peak solitons induced by higher-order effects in an erbium-doped fiber system

2016 ◽  
Vol 70 (9) ◽  
Author(s):  
Yang Ren ◽  
Zhan-Ying Yang ◽  
Chong Liu ◽  
Wen-Hao Xu ◽  
Wen-Li Yang
Keyword(s):  
Higher Order ◽  
Order Effects ◽  
Fiber System ◽  
Erbium Doped ◽  
Higher Order Effects

Localised Nonlinear Waves in the Three-Component Coupled Hirota Equations

2017 ◽  
Vol 72 (11) ◽  
pp. 1053-1070 ◽  
Author(s):  
Tao Xu ◽  
Yong Chen
Keyword(s):  
Darboux Transformation ◽  
Dark Soliton ◽  
Lax Pair ◽  
Higher Order ◽  
Bright Soliton ◽  
Order Effects ◽  
Vector Solution ◽  
Hybrid Solutions ◽  
Three Components ◽  
Hirota Equations

AbstractWe construct the Lax pair and Darboux transformation for the three-component coupled Hirota equations including higher-order effects such as third-order dispersion, self-steepening, and stimulated Raman scattering. A special vector solution of the Lax pair with 4×4 matrices for the three-component Hirota system is elaborately generated, based on this vector solution, various types of mixed higher-order localised waves are derived through the generalised Darboux transformation. Instead of considering various arrangements of the three potential functions q1, q2, and q3, here, the same combination is considered as the same type solution. The first- and second-order localised waves are mainly discussed in six mixed types: (1) the hybrid solutions degenerate to the rational ones and three components are all rogue waves; (2) two components are hybrid solutions between rogue wave (RW) and breather (RW+breather), and one component is interactional solution between RW and dark soliton (RW+dark soliton); (3) two components are RW+dark soliton, and one component is RW+bright soliton; (4) two components are RW+breather, and one component is RW+bright soliton; (5) two components are RW+dark soliton, and one component is RW+bright soliton; (6) three components are all RW+breather. Moreover, these nonlinear localised waves merge with each other by increasing the absolute values of two free parameters α, β. These results further uncover some striking dynamic structures in the multicomponent coupled system.

Sign in / Sign up

Export Citation Format

Share Document