scholarly journals Soliton solutions for variable coefficient nonlinear Schr?dinger equation for optical fiber and their application

2006 ◽  
Vol 55 (8) ◽  
pp. 3805
Author(s):  
Zong Feng-De ◽  
Dai Chao-Qing ◽  
Yang Qin ◽  
Zhang Jie-Fang
Keyword(s):  
Optical Fiber ◽  
Variable Coefficient ◽  
Soliton Solutions ◽  
Dinger Equation

Bilinear forms and soliton solutions for a (2 + 1)-dimensional variable-coefficient nonlinear Schrödinger equation in an optical fiber

2020 ◽  
Vol 34 (30) ◽  
pp. 2050336
Author(s):  
Dong Wang ◽  
Yi-Tian Gao ◽  
Jing-Jing Su ◽  
Cui-Cui Ding
Keyword(s):  
Schrödinger Equation ◽  
Optical Fiber ◽  
Nonlinear Schrödinger Equation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Nonlinear Schrodinger Equation ◽  
Bilinear Forms ◽  
Dimensional Variable

In this paper, under investigation is a (2 + 1)-dimensional variable-coefficient nonlinear Schrödinger equation, which is introduced to the study of an optical fiber, where [Formula: see text] is the temporal variable, variable coefficients [Formula: see text] and [Formula: see text] are related to the group velocity dispersion, [Formula: see text] and [Formula: see text] represent the Kerr nonlinearity and linear term, respectively. Via the Hirota bilinear method, bilinear forms are obtained, and bright one-, two-, three- and N-soliton solutions as well as dark one- and two-soliton solutions are derived, where [Formula: see text] is a positive integer. Velocities and amplitudes of the bright/dark one solitons are obtained via the characteristic-line equations. With the graphical analysis, we investigate the influence of the variable coefficients on the propagation and interaction of the solitons. It is found that [Formula: see text] can only affect the phase shifts of the solitons, while [Formula: see text], [Formula: see text] and [Formula: see text] determine the amplitudes and velocities of the bright/dark solitons.

Bilinear forms and dark-soliton solutions for a fifth-order variable-coefficient nonlinear Schrödinger equation in an optical fiber

2016 ◽  
Vol 30 (24) ◽  
pp. 1650312 ◽  
Author(s):  
Chen Zhao ◽  
Yi-Tian Gao ◽  
Zhong-Zhou Lan ◽  
Jin-Wei Yang ◽  
Chuan-Qi Su
Keyword(s):  
Schrödinger Equation ◽  
Optical Fiber ◽  
Nonlinear Schrödinger Equation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Bilinear Forms ◽  
Order Variable ◽  
Fifth Order

In this paper, a fifth-order variable-coefficient nonlinear Schrödinger equation is investigated, which describes the propagation of the attosecond pulses in an optical fiber. Via the Hirota’s method and auxiliary functions, bilinear forms and dark one-, two- and three-soliton solutions are obtained. Propagation and interaction of the solitons are discussed graphically: We observe that the solitonic velocities are only related to [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the coefficients of the second-, third-, fourth- and fifth-order terms, respectively, with [Formula: see text] being the scaled distance, while the solitonic amplitudes are related to [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] as well as the wave number. When [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are the constants, or the linear, quadratic and trigonometric functions of [Formula: see text], we obtain the linear, parabolic, cubic and periodic dark solitons, respectively. Interactions between (among) the two (three) solitons are depicted, which can be regarded to be elastic because the solitonic amplitudes remain unchanged except for some phase shifts after each interaction in an optical fiber.

Dark solitons for a variable-coefficient Kundu–Eckhaus equation in an inhomogeneous optical fiber with the relevant Lax pair and binary Darboux transformations

2019 ◽  
Vol 33 (01) ◽  
pp. 1850418 ◽  
Author(s):  
Ze Zhang ◽  
Bo Tian ◽  
Han-Peng Chai ◽  
Hui-Min Yin ◽  
Chen-Rong Zhang
Keyword(s):  
Optical Fiber ◽  
Group Velocity ◽  
Variable Coefficient ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Darboux Transformations ◽  
Dark Solitons ◽  
The One

In this paper, we study a Kundu–Eckhaus equation with variable coefficients, which describes the ultra-short optical pulses in an inhomogeneous optical fiber. We construct the Lax pair under certain variable-coefficient constraints. With the gauge transformation, one/N-fold binary Darboux transformations and limit forms of the one-fold binary Darboux transformation are obtained. Based on such transformations, one/N-dark (N = 2,3, [Formula: see text]) soliton solutions under those constraints are derived. Linear, periodic and parabolic dark solitons are presented, and numerical simulations are used to investigate the influence of the group velocity dispersion on the structures of the one-dark solitons. Based on the two-dark soliton solutions under certain variable-coefficient constraints, we also discuss the influence of the group velocity dispersion on the structures of the two-dark solitons. Head-on and overtaking collisions between the two linear, parabolic and cubic-type dark solitons are presented.

Dark solitons for a variable-coefficient higher-order nonlinear Schrödinger equation in the inhomogeneous optical fiber

2017 ◽  
Vol 31 (12) ◽  
pp. 1750065 ◽  
Author(s):  
Yan Sun ◽  
Bo Tian ◽  
Xiao-Yu Wu ◽  
Lei Liu ◽  
Yu-Qiang Yuan
Keyword(s):  
Schrödinger Equation ◽  
Optical Fiber ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Dark Solitons ◽  
Order Dispersion

Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with [Formula: see text], [Formula: see text] and [Formula: see text], which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficients, we obtain the parabolic, periodic and V-shaped dark solitons. Head-on and overtaking collisions are depicted via the dark two soliton solutions. Velocities of the dark solitons are linearly related to [Formula: see text], [Formula: see text] and [Formula: see text], respectively, while the amplitudes of the dark solitons are not related to such variable coefficients.

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