scholarly journals Conservation laws of femtosecond pulse propagation described by generalized nonlinear Schrödinger equation with cubic nonlinearity

2021 ◽  
Vol 182 ◽  
pp. 366-396
Author(s):  
Vyacheslav A. Trofimov ◽  
Svetlana Stepanenko ◽  
Alexander Razgulin
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Femtosecond Pulse ◽  
Pulse Propagation ◽  
Nonlinear Schrodinger Equation ◽  
Cubic Nonlinearity ◽  
Nonlinear Schrödinger ◽  
Generalized Nonlinear Schrödinger Equation

ANALYTICAL SOLUTIONS FOR THE VARIATIONAL EQUATIONS DERIVED FOR THE NONLINEAR SCHRÖDINGER EQUATION: DISPERSION-MANAGED FIBER SYSTEM

2008 ◽  
Vol 17 (03) ◽  
pp. 285-297 ◽  
Author(s):  
ABDOSLLAM M. ABOBAKER ◽  
A. B. MOUBISSI ◽  
TH. B. EKOGO ◽  
K. NAKKEERAN
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Pulse Width ◽  
Schrodinger Equation ◽  
Pulse Propagation ◽  
Nonlinear Schrodinger Equation ◽  
Fiber System ◽  
Variational Equations ◽  
Nonlinear Schrödinger ◽  
The Given

We consider the nonlinear Schrödinger equation which governs the pulse propagation in dispersion-managed (DM) optical fiber transmission systems. Using a generalized form of ansatz function for the shape of the pulse, we derive the variational equations. For a particular case of DM fiber systems when the Hamiltonian is zero, we solve the variational equations analytically and obtain the expressions for the pulse energy, amplitude, width and chirp. Finally for Gaussian and hyperbolic secant shaped pulses, we show through numerical simulations that the analytically calculated energy (for the given pulse width and chirp) is good enough to support the periodic evolution of the DM soliton. The simulations are carried out for conventional and dense DM fiber systems for both lossless and lossy cases.

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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