Modulational instability in the cubic–quintic nonlinear Schrödinger equation through the variational approach

2007 ◽  
Vol 275 (2) ◽  
pp. 421-428 ◽  
Author(s):  
Fabien II Ndzana ◽  
Alidou Mohamadou ◽  
Timoléon Crépin Kofané
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Variational Approach ◽  
Schrodinger Equation ◽  
Modulational Instability ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Quintic Nonlinear Schrödinger Equation

A VARIATIONAL APPROACH IN THE DISSIPATIVE CUBIC-QUINTIC NONLINEAR SCHRÖDINGER EQUATION

2002 ◽  
Vol 16 (01n02) ◽  
pp. 27-32 ◽  
Author(s):  
DAGOBERTO S. FREITAS ◽  
JAIRO R. DE OLIVEIRA
Keyword(s):  
Schrödinger Equation ◽  
Inverse Scattering ◽  
Nonlinear Schrödinger Equation ◽  
Variational Approach ◽  
Schrodinger Equation ◽  
Pulse Propagation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Nonlinear Fiber ◽  
Quintic Nonlinear Schrödinger Equation

The properties of pulse propagation in a nonlinear fiber including a linear damped term added in the nonlinear Schrödinger equation with cubic and quintic terms is analyzed analytically. We apply the variational modified approach based on the Lagrangian that describes the dynamic of a system and, with a suitable trial function, we obtain a solution which is as accurate as a pertubative solution found by inverse scattering transformation in earlier works. As a result, we show that the quintic term can retain the pulse propagation more stably and in a greater time in optical fiber.

scholarly journals On the Existence of Bright Solitons in Cubic-Quintic Nonlinear Schrödinger Equation with Inhomogeneous Nonlinearity

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Juan Belmonte-Beitia
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Bifurcation Theory ◽  
Schrodinger Equation ◽  
Chemical Potential ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Bose Einstein ◽  
Quintic Nonlinear Schrödinger Equation

We give a proof of the existence of stationary bright soliton solutions of the cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity. By using bifurcation theory, we prove that the norm of the positive solution goes to zero as the parameterλ, called chemical potential in the Bose-Einstein condensates' literature, tends to zero. Moreover, we solve the time-dependent cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearities by using a numerical method.

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