Vector semirational rogue waves for the coupled nonlinear Schrödinger equations with the higher-order effects in the elliptically birefringent optical fiber

2018 ◽  
Vol 30 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Cui-Cui Ding ◽  
Yi-Tian Gao ◽  
Jing-Jing Su ◽  
Gao-Fu Deng ◽  
Shu-Liang Jia
Keyword(s):  
Optical Fiber ◽  
Rogue Waves ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Order Effects ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrodinger Equations ◽  
Birefringent Optical Fiber ◽  
Higher Order Effects

scholarly journals Modulational instability, beak-shaped rogue waves, multi-dark-dark solitons and dynamics in pair-transition-coupled nonlinear Schrödinger equations

2017 ◽  
Vol 473 (2203) ◽  
pp. 20170243 ◽  
Author(s):  
Guoqiang Zhang ◽  
Zhenya Yan ◽  
Xiao-Yong Wen
Keyword(s):  
Modulational Instability ◽  
Coupled Model ◽  
Rogue Waves ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Dark Solitons ◽  
Nonlinear Schrodinger Equations

The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N -fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial–temporal distribution structures including triangular, pentagonal, ‘claw-like’ and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.

Mixed interaction solutions for the coupled nonlinear Schrödinger equations

2021 ◽  
pp. 2150004
Author(s):  
Yaning Tang ◽  
Jiale Zhou
Keyword(s):  
Darboux Transformation ◽  
Rogue Waves ◽  
Transformation Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Interaction Solutions ◽  
Nonlinear Schrodinger Equations

We investigate the mixed interaction solutions of the coupled nonlinear Schrödinger equations (CNLSE) through the Darboux transformation method. First of all, we derive the nonsingular localized wave solutions for two cases of CNLSE by the Darboux transformation method and matrix analysis method. Furthermore, we take a limit technique to deduce rogue waves and divide the rogue waves into four categories through analyzing their dynamic behaviors. Based on the obtained theorems, the Darboux transformations are presented to solve interaction solutions between distinct nonlinear waves. In this paper, we mainly study four types. Finally, the dynamic characteristics of the constructed these solutions are analyzed by sequences of interesting figures plotted with the help of Maple.

Modeling optical solitons in a practical lossy fiber

2000 ◽  
Vol 78 (12) ◽  
pp. 1087-1090
Author(s):  
M F Mahmood
Keyword(s):  
Optical Fiber ◽  
Variational Formulation ◽  
Analytical Investigation ◽  
Optical Solitons ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Optical Pulses ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

An analytical investigation is presented that is based on the Lagrangian variational formulation of the interaction of two orthogonally polarized optical pulses. The pulses are governed by a pair of coupled nonlinear Schrödinger equations in a practical lossy optical fiber. PACS Nos.: 03.40Kf, 42.65Tg, 42.81Dp

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