Integrability and soliton solutions for an N-coupled nonlinear Schrödinger system in optical fibers

2013 ◽  
Vol 392 (19) ◽  
pp. 4532-4542 ◽  
Author(s):  
Ming Wang ◽  
Bo Tian ◽  
Min Li ◽  
Wen-Rui Shan
Keyword(s):  
Optical Fibers ◽  
Soliton Solutions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

Exact Localized and Periodic Solutions of the Ablowitz-Ladik Discrete Nonlinear Schrödinger System

2005 ◽  
Vol 60 (8-9) ◽  
pp. 573-582 ◽  
Author(s):  
Xian-jing Lai ◽  
Jie-fang Zhang
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger System ◽  
Pacs 02.30 ◽  
Schrödinger System ◽  
Jacobian Functions

We have studied, analytically, the Ablowitz-Ladik discrete nonlinear Schr¨odinger system. We have found a set of exact solutions which includes as particular cases periodic solutions in terms of elliptic Jacobian functions, bright and dark soliton solutions, and quasi-periodic solutions. We have also found the range of parameters where each exact solution exists. - PACS: 02.30.Jr, 05.45.Yv, 42.65.Tg, 02.30.Gp.

Dark–dark and bright–dark solitons for a (2+1)-dimensional variable-coefficient nonlinear Schrödinger system in a graded-index waveguide

2020 ◽  
Vol 34 (17) ◽  
pp. 2050183
Author(s):  
Jie Zhang ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
Yu-Qiang Yuan ◽  
He-Yuan Tian ◽  
...  
Keyword(s):  
Variable Coefficient ◽  
Soliton Solutions ◽  
Beam Width ◽  
Dark Soliton ◽  
Nonlinear Schrödinger ◽  
Graded Index ◽  
Dark Solitons ◽  
Nonlinear Schrödinger System ◽  
Dimensional Variable ◽  
Schrödinger System

In this letter, we study a (2[Formula: see text]+[Formula: see text]1)-dimensional variable-coefficient nonlinear Schrödinger system, which describes an optical beam inside the two-dimensional graded-index waveguide with polarization effects. Through the Kadomtsev–Petviashvili hierarchy reduction, the [Formula: see text] dark–dark soliton and [Formula: see text] bright-dark soliton solutions in terms of the Gramian are obtained, where [Formula: see text] is a positive integer. We analyze the interaction and propagation of the dark–dark solitons graphically. With the different values of the diffraction coefficient [Formula: see text], periodic-, cubic- and parabolic-shaped dark–dark solitons are derived. With the different values of the gain/loss coefficient [Formula: see text], periodic- and arctangent-profile background waves are obtained. Moreover, we discuss the effects from the dimensionless beam width [Formula: see text], [Formula: see text] and [Formula: see text] on the solitons and background waves: Shapes of the solitons are affected by [Formula: see text] and [Formula: see text], while profiles of the background waves are affected by [Formula: see text] and [Formula: see text].

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.

Soliton Solutions, Pairwise Collisions and Partially Coherent Interactions for A Generalized (1+1)-Dimensional Coupled Nonlinear Schrödinger System via Symbolic Computation

2008 ◽  
Vol 63 (10-11) ◽  
pp. 679-687
Author(s):  
Li-Li Li ◽  
Bo Tian ◽  
Hai-Qiang Zhang ◽  
Xing Lü ◽  
Wen-Jun Liu
Keyword(s):  
Symbolic Computation ◽  
Soliton Solutions ◽  
Nonlinear Interactions ◽  
Elastic Solids ◽  
Bilinear Method ◽  
Nonlinear Schrödinger ◽  
Partially Coherent ◽  
Nonlinear Schrödinger System ◽  
Potential Applications ◽  
Schrödinger System

With the aid of symbolic computation, we investigate a generalized (1+1)-dimensional coupled nonlinear Schrödinger system with mixed nonlinear interactions, which has potential applications in nonlinear optics and elastic solids. The exact analytical one-, two-, and three-soliton solutions are firstly obtained by employing the bilinear method under two constraints. Some main propagation and interaction properties of the solitons are discussed simultaneously.Moreover, some figures are plotted to graphically analyze the pairwise collisions and partially coherent interactions of three solitons.

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.

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