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

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].

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

Zeitschrift für Naturforschung A ◽

10.1515/zna-2017-0148 ◽

2017 ◽

Vol 72 (8) ◽

pp. 779-787 ◽

Cited By ~ 6

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.

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

Zeitschrift für Naturforschung A ◽

10.1515/zna-2005-8-904 ◽

2005 ◽

Vol 60 (8-9) ◽

pp. 573-582 ◽

Cited By ~ 2

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.

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