On instability for the quintic nonlinear Schrodinger equation of some approximate periodic solutions

2012 ◽  
Vol 61 (6) ◽  
pp. 2053-2083
Author(s):  
Jeremy Marzuola ◽  
Scipio Cuccagna
Keyword(s):  
Schrödinger Equation ◽  
Periodic Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Quintic Nonlinear Schrödinger Equation

Periodic and solitary waves of the cubic–quintic nonlinear Schrödinger equation

2004 ◽  
Vol 70 (4) ◽  
pp. 415-429 ◽  
Author(s):  
LIU HONG ◽  
ROBERT BEECH ◽  
FREDERICK OSMAN ◽  
HE XIAN-TU ◽  
LOU SEN-YUE ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Periodic Solutions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Fast Ions ◽  
High Intensity Laser ◽  
Intensity Laser ◽  
Quintic Nonlinear Schrödinger Equation

This paper presents the possible periodic solutions and the solitons of the cubic–quintic nonlinear Schrödinger equation. Corresponding to five types of different structures of the pseudo-potentials, five types of periodic solutions are given explicitly. Five types of solitons are also obtained explicitly from the limiting procedures of the periodic solutions. This will benefit the study of the generation of fast ions or electrons, which are produced from the soliton breaking when the plasma is irradiated a high-intensity laser pulse.

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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