Exact solutions for the nonlinear Schr�dinger equation with power law nonlinearity

2012 ◽  
Vol 1 (1) ◽  
pp. 7-16 ◽  
Author(s):  
N. Taghizadeh ◽  
M. Mirzazadeh ◽  
A.Samiei Paghaleh
Keyword(s):  
Exact Solutions ◽  
Power Law ◽  
Dinger Equation

scholarly journals Cosmological constant in chameleon Brans–Dicke theory

2019 ◽  
Vol 28 (01) ◽  
pp. 1950022 ◽  
Author(s):  
Yousef Bisabr
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Exact Solutions ◽  
Effective Mass ◽  
Potential Function ◽  
Power Law ◽  
Exponential Form ◽  
First Case ◽  
Different Types

We consider a generalized Brans–Dicke model in which the scalar field has a self-interacting potential function. The scalar field is also allowed to couple nonminimally with the matter part. We assume that it has a chameleon behavior in the sense that it acquires a density-dependent effective mass. We consider two different types of matter systems which couple with the chameleon, dust and vacuum. In the first case, we find a set of exact solutions when the potential has an exponential form. In the second case, we find a power-law exact solution for the scale factor. In this case, we will show that the vacuum density decays during expansion due to coupling with the chameleon.

A METHOD OF GENERATING EXACT SOLUTIONS OF THE TIME-DEPENDENT SCHRÖDINGER EQUATION WITH TIME-DEPENDENT MASS

2002 ◽  
Vol 17 (24) ◽  
pp. 1567-1573
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Large Class ◽  
Power Law ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Stationary Schrödinger Equation ◽  
Dependent Mass

Extending the method presented in our previous paper,12 we map the time-dependent Schrödinger equation (TDSE) with time-dependent mass on a stationary Schrödinger equation for a nonconstant potential. On solving the latter, we can thus generate a large class of exact solutions of the original TDSE. Several examples are given, including potentials of power-law and modified Pöschl–Teller type.

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