Modulational instability and discrete breathers in the discrete cubic–quintic nonlinear Schrödinger equation

2007 ◽  
Vol 232 (1) ◽  
pp. 54-61 ◽  
Author(s):  
F.Kh. Abdullaev ◽  
A. Bouketir ◽  
A. Messikh ◽  
B.A. Umarov
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Modulational Instability ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Discrete Breathers ◽  
Quintic Nonlinear Schrödinger Equation

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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