Exact analytical solutions for the variational equations derived from the nonlinear Schrödinger equation

2007 ◽  
Vol 76 (2) ◽  
Author(s):  
A. B. Moubissi ◽  
K. Nakkeeran ◽  
Abdosllam M. Abobaker
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Variational Equations ◽  
Exact Analytical Solutions ◽  
Nonlinear Schrödinger

Exact analytical solutions of higher-order nonlinear Schrödinger equation

Optik ◽  
2017 ◽  
Vol 131 ◽  
pp. 438-445 ◽  
Author(s):  
Hongcheng Wang ◽  
Jianchu Liang ◽  
Guihua Chen ◽  
Ling Zhou ◽  
Dongxiong Ling ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Exact Analytical Solutions ◽  
Nonlinear Schrödinger

A GENERALIZED SUB-EQUATION EXPANSION METHOD AND ITS APPLICATION TO THE NONLINEAR SCHRÖDINGER EQUATION IN INHOMOGENEOUS OPTICAL FIBER MEDIA

2007 ◽  
Vol 18 (07) ◽  
pp. 1187-1201 ◽  
Author(s):  
BIAO LI
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Analytical Solutions ◽  
Elliptic Function ◽  
Schrodinger Equation ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Jacobi Elliptic Function ◽  
Exact Analytical Solutions ◽  
Nonlinear Schrödinger

In this paper, a generalized sub-equation expansion method is presented for constructing some exact analytical solutions of nonlinear partial differential equations. Making use of the method and symbolic computation, we investigate the inhomogeneous nonlinear Schrödinger equation (INLSE) with the loss/gain and the frequency chirping and obtain rich exact analytical solutions. From our results, many known results of some nonlinear Schrödinger equations can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. With computer simulation, the main soliton features of bright and dark solitons, Jacobi elliptic function solutions, and Weierstrass elliptic function solutions are shown by some figures. Nonlinear dynamics of the chirped soliton pulses is also investigated under the different regimes of soliton management. The method developed does provide a systematic way to generate various exact analytical solutions for INLSE with varying coefficients.

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 New Optical Soliton Solutions to the Fractional Hyperbolic Nonlinear Schrödinger Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ahmad Sharif
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Integration Method ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Exact Analytical Solutions ◽  
Nonlinear Schrödinger ◽  
And Performance ◽  
Mathematica Software

This paper is aimed at investigating the soliton solutions of the hyperbolic nonlinear Schrödinger equation. Exact analytical solutions of the model are acquired through applying an integration method, namely, the Sine-Gordon method. It is observed that the method is able to efficiently determine the exact solutions for this equation. Graphical simulations corresponding to some of the results obtained in the paper are also drawn. These results can help us better understand the behavior and performance of this model. The procedure implemented in this paper can be recommended in solving other equations in the field. All calculations and graphing are performed using powerful symbolic computational packages in Mathematica software.

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