Rogue waves for a generalized nonlinear Schrödinger equation with distributed coefficients in a monomode optical fiber

2018 ◽  
Vol 107 ◽  
pp. 266-274 ◽  
Author(s):  
Yan Sun ◽  
Bo Tian ◽  
Lei Liu ◽  
Xiao-Yu Wu
Keyword(s):  
Schrödinger Equation ◽  
Optical Fiber ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Generalized Nonlinear Schrödinger Equation

Breathers and rogue waves for an eighth-order nonlinear Schrödinger equation in an optical fiber

2017 ◽  
Vol 31 (05) ◽  
pp. 1750035 ◽  
Author(s):  
Wen-Qiang Hu ◽  
Yi-Tian Gao ◽  
Chen Zhao ◽  
Zhong-Zhou Lan
Keyword(s):  
Schrödinger Equation ◽  
Optical Fiber ◽  
Nonlinear Schrödinger Equation ◽  
Spectral Parameter ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Rogue Waves ◽  
Nonlinear Schrodinger Equation ◽  
Eighth Order ◽  
Nonlinear Schrödinger

In this paper, an eighth-order nonlinear Schrödinger equation is investigated in an optical fiber, which can be used to describe the propagation of ultrashort nonlinear pulses. Lax pair and infinitely-many conservation laws are derived to verify the integrability of this equation. Via the Darboux transformation and generalized Darboux transformation, the analytic breather and rogue wave solutions are obtained. Influence of the coefficients of operators in this equation, which represent different order nonlinearity, and the spectral parameter on the propagation and interaction of the breathers and rogue waves is also discussed. We find that (i) the periodic of the breathers decreases as the augment of the spectral parameter; (ii) the coefficients of operators change the compressibility and periodic of the breathers, and can affect the interaction range and temporal–spatial distribution of the rogue waves.

scholarly journals ASYMPTOTIC STABILITY OF NONLINEAR SCHRÖDINGER EQUATIONS WITH POTENTIAL

2005 ◽  
Vol 17 (10) ◽  
pp. 1143-1207 ◽  
Author(s):  
ZHOU GANG ◽  
I. M. SIGAL
Keyword(s):  
Asymptotic Stability ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Nonlinear Schrodinger Equation ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Generalized Nonlinear Schrödinger Equation

We prove asymptotic stability of trapped solitons in the generalized nonlinear Schrödinger equation with a potential in dimension 1 and for even potential and even initial conditions.

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