A new approach to the analytic soliton solutions for the variable-coefficient higher-order nonlinear Schrödinger model in inhomogeneous optical fibers

2010 ◽  
Vol 57 (4) ◽  
pp. 309-315 ◽  
Author(s):  
Wen-Jun Liu ◽  
Bo Tian ◽  
Pan Wang ◽  
Yan Jiang ◽  
Kun Sun ◽  
...  
Keyword(s):  
Optical Fibers ◽  
Variable Coefficient ◽  
Soliton Solutions ◽  
Higher Order ◽  
New Approach ◽  
Nonlinear Schrödinger

N-dark–dark solitons for the coupled higher-order nonlinear Schrödinger equations in optical fibers

2017 ◽  
Vol 31 (33) ◽  
pp. 1750305 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Yue Wang
Keyword(s):  
Optical Fibers ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Dark Solitons ◽  
Nonlinear Schrodinger Equations

In this paper, we construct the binary Darboux transformation on the coupled higher-order dispersive nonlinear Schrödinger equations in optical fibers. We present the N-fold iterative transformation in terms of the determinants. By the limit technique, we derive the N-dark–dark soliton solutions from the non-vanishing background. Based on the obtained solutions, we find that the collision mechanisms of dark vector solitons exhibit the standard elastic collisions in both two components.

ANALYTIC DARK SOLITON SOLUTIONS FOR A GENERALIZED VARIABLE-COEFFICIENT HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION IN OPTICAL FIBERS USING SYMBOLIC COMPUTATION

2011 ◽  
Vol 25 (04) ◽  
pp. 499-509 ◽  
Author(s):  
XIANG-HUA MENG ◽  
ZHI-YUAN SUN ◽  
CHUN-YI ZHANG ◽  
BO TIAN
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Symbolic Computation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Bilinear Method ◽  
Nonlinear Schrödinger

In this paper, a generalized variable-coefficient nonlinear Schrödinger equation with higher-order and gain/loss effects which can be used to describe the femtosecond pulse propagation is analytically investigated via symbolic computation. Under sets of coefficient constraints, such an equation is transformed into a completely integrable constant-coefficient higher-order nonlinear Schrödinger equation. Furthermore, through the transformation, the dark one- and two-soliton solutions for the generalized variable-coefficient higher-order nonlinear Schrödinger equation are derived by means of the bilinear method.

Double Wronskian Solution and Conservation Laws for a Generalized Variable-Coefficient Higher-Order Nonlinear Schrödinger Equation in Optical Fibers

2009 ◽  
Vol 64 (7-8) ◽  
pp. 411-419
Author(s):  
Xiang-Hua Meng ◽  
Hong-Wu Zhu ◽  
Juan Li ◽  
Zhen-Zhi Yao ◽  
Bo Tian
Keyword(s):  
Conservation Laws ◽  
Optical Fibers ◽  
Infinite Number ◽  
Variable Coefficient ◽  
Optical Transmission ◽  
Higher Order ◽  
Wronskian Technique ◽  
Nonlinear Schrödinger ◽  
Higher Power ◽  
Double Wronskian

AbstractWith applications in the higher-power and femtosecond optical transmission regime, a generalized variable-coefficient higher-order nonlinear Schrödinger (VC-HNLS) equation is analytically investigated. The multi-solitonic solutions of the generalized VC-HNLS equation in double Wronskian form is constructed and further verified using the Wronskian technique. Additionally, an infinite number of conservation laws for such an equation are presented. Finally, discussions and conclusions on results are made with figures plotted.

Sign in / Sign up

Export Citation Format

Share Document