Multilinear Eigenfunction Estimates for the Harmonic Oscillator and the Nonlinear Schrödinger Equation with the Harmonic Potential

2009 ◽  
Vol 10 (4) ◽  
pp. 673-709
Author(s):  
Takafumi Akahori ◽  
Kenichi Ito
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Harmonic Potential ◽  
Nonlinear Schrödinger ◽  
Eigenfunction Estimates

The Nonlinear Schrödinger Equation with a Strongly Anisotropic Harmonic Potential

2005 ◽  
Vol 37 (1) ◽  
pp. 189-199 ◽  
Author(s):  
Naoufel Ben Abdallah ◽  
Florian Méhats ◽  
Christian Schmeiser ◽  
Rada M. Weishäupl
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Harmonic Potential ◽  
Nonlinear Schrödinger

Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential: I. Bright solitons

2005 ◽  
Vol 35 (9) ◽  
pp. 778-786 ◽  
Author(s):  
C Hernandez Tenorio ◽  
E Villagran Vargas ◽  
Vladimir N Serkin ◽  
M Aguero Granados ◽  
T L Belyaeva ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Harmonic Potential ◽  
Nonlinear Schrödinger ◽  
Bright Solitons

Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential: II. Dark Solitons

2005 ◽  
Vol 35 (10) ◽  
pp. 929-937 ◽  
Author(s):  
C Hernandez Tenorio ◽  
E Villagran Vargas ◽  
Vladimir N Serkin ◽  
M Aguero Granados ◽  
T L Belyaeva ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Harmonic Potential ◽  
Nonlinear Schrödinger ◽  
Dark Solitons

scholarly journals An Approximate Analytical Solution of the Nonlinear Schrödinger Equation with Harmonic Oscillator Using Homotopy Perturbation Method and Laplace-Adomian Decomposition Method

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Emad K. Jaradat ◽  
Omar Alomari ◽  
Mohammad Abudayah ◽  
Ala’a M. Al-Faqih
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

The Laplace-Adomian Decomposition Method (LADM) and Homotopy Perturbation Method (HPM) are both utilized in this research in order to obtain an approximate analytical solution to the nonlinear Schrödinger equation with harmonic oscillator. Accordingly, nonlinear Schrödinger equation in both one and two dimensions is provided to illustrate the effects of harmonic oscillator on the behavior of the wave function. The available literature does not provide an exact solution to the problem presented in this paper. Nevertheless, approximate analytical solutions are provided in this paper using LADM and HPM methods, in addition to comparing and analyzing both solutions.

GLOBAL WELL-POSEDNESS AND INSTABILITY OF A NONLINEAR SCHRÖDINGER EQUATION WITH HARMONIC POTENTIAL

2014 ◽  
Vol 98 (1) ◽  
pp. 78-103
Author(s):  
T. SAANOUNI
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Harmonic Potential ◽  
Well Posedness ◽  
Potential Well ◽  
Nonlinear Schrödinger ◽  
The Cauchy Problem ◽  
Two Space Dimensions

AbstractThis paper is concerned with the Cauchy problem for a nonlinear Schrödinger equation with a harmonic potential and exponential growth nonlinearity in two space dimensions. In the defocusing case, global well-posedness is obtained. In the focusing case, existence of nonglobal solutions is discussed via potential-well arguments.

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