Bilinear forms and bright-dark solitons for a coupled nonlinear Schrödinger system with variable coefficients in an inhomogeneous optical fiber

2019 ◽  
Vol 62 ◽  
pp. 202-212 ◽  
Author(s):  
Yang Han ◽  
Bo Tian ◽  
Yu-Qiang Yuan ◽  
Chen-Rong Zhang ◽  
Su-Su Chen
Keyword(s):  
Optical Fiber ◽  
Variable Coefficients ◽  
Bilinear Forms ◽  
Nonlinear Schrödinger ◽  
Dark Solitons ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

Vector Dark Solitons for a Coupled Nonlinear Schrödinger System with Variable Coefficients in an Inhomogeneous Optical Fibre

2017 ◽  
Vol 72 (8) ◽  
pp. 779-787 ◽  
Author(s):  
Lei Liu ◽  
Bo Tian ◽  
Xiao-Yu Wu ◽  
Yu-Qiang Yuan
Keyword(s):  
Optical Fibre ◽  
Bound States ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Variable Coefficients ◽  
Nonlinear Schrödinger ◽  
Dark Solitons ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

AbstractStudied in this paper are the vector dark solitons for a coupled nonlinear Schrödinger system with variable coefficients, which can be used to describe the pulse simultaneous propagation of the M-field components in an inhomogeneous optical fibre, where M is a positive integer. When M=2, under the integrable constraint, we construct the nondegenerate N-dark-dark soliton solutions in terms of the Gramian through the Kadomtsev–Petviashvili hierarchy reduction. With the help of analytic analysis, a vector one soliton with varying amplitude and velocity is studied. Interactions and bound states between the two solitons under different group velocity dispersion and amplification/absorption coefficients are presented. Moreover, we extend our analysis to any M to obtain the nondegenerate vector N-dark soliton solutions.

Bright solitons and their interactions of the (3 + 1)-dimensional coupled nonlinear Schrödinger system for an optical fiber

2015 ◽  
Vol 29 (35n36) ◽  
pp. 1550245 ◽  
Author(s):  
Ya Sun ◽  
Bo Tian ◽  
Yu-Feng Wang ◽  
Yun-Po Wang ◽  
Zhi-Ruo Huang
Keyword(s):  
Optical Fiber ◽  
Soliton Solutions ◽  
Auxiliary Function ◽  
Bilinear Forms ◽  
Soliton Propagation ◽  
Nonlinear Schrödinger ◽  
Elastic Interactions ◽  
Bright Solitons ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

Under investigation in this paper is the [Formula: see text]-dimensional coupled nonlinear Schrödinger system for an optical fiber with birefringence. With the Hirota method, bilinear forms of the system are derived via an auxiliary function, and the bright one- and two-soliton solutions are constructed. Based on those soliton solutions, soliton propagation and interaction are investigated analytically and graphically. Non-singular cases of the bright one-soliton solutions are presented, from which the single-peak and two-peak solitons can arise, respectively. Through the analysis on the bright two-soliton solutions, the elastic and inelastic interactions are investigated. Three kinds of the elastic interactions are presented, between the two one-peak solitons, a one-peak soliton and a two-peak soliton, and the two two-peak solitons.

scholarly journals Vector Solitons of a Coupled Schrödinger System with Variable Coefficients

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Juan Carlos Muñoz Grajales
Keyword(s):  
Numerical Simulations ◽  
Finite Energy ◽  
Variable Coefficients ◽  
Soliton Equations ◽  
Nonlinear Schrödinger ◽  
Coupled Schrödinger System ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

We show the existence of waveforms of finite-energy (vector solitons) for a coupled nonlinear Schrödinger system with inhomogeneous coefficients. Furthermore, some of these solutions are approximated using a Newton-type iteration, combined with a collocation-spectral strategy to discretize the corresponding soliton equations. Some numerical simulations concerned with analysis of a collision of two oncoming vector solitons of the system are also performed.

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