Nonautonomous multi-peak solitons and modulation instability for a variable-coefficient nonlinear Schrödinger equation with higher-order effects

2017 ◽  
Vol 90 (3) ◽  
pp. 2221-2230 ◽  
Author(s):  
Liu-Ying Cai ◽  
Xin Wang ◽  
Lei Wang ◽  
Min Li ◽  
Yong Liu ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Variable Coefficient ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Order Effects ◽  
Nonlinear Schrödinger ◽  
Higher Order Effects

Grey solitons and soliton interaction of higher nonlinear Schrödinger equation

2010 ◽  
Vol 88 (1) ◽  
pp. 9-14 ◽  
Author(s):  
Qiu-Yan Li ◽  
Zai-Dong Li ◽  
Peng-Bin He ◽  
Wei-Wei Song ◽  
Guangsheng Fu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Continuous Wave ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Order Effects ◽  
Nonlinear Schrödinger ◽  
Grey Soliton ◽  
Higher Order Effects

In this paper, the higher nonlinear Schrödinger equation is solved by the Hirota method. As an example, the exact grey one- and two-soliton solutions in explicit forms are generated analytically under the continuous-wave background. The results reveal that the velocity of the grey soliton is clearly affected by the higher order effects, yet the grey soliton propagates without any change in their shape and intensity. The higher order term and the phase velocity play the important role for the maximum valley of grey soliton, i.e., the intensity of grey soliton. For the black soliton, the velocity of soliton is determined only by the higher order effects. The analysis of the asymptotic behavior of a two grey soliton solution shows the collision is elastic.

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.

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