Nonlinear Schrödinger equation with harmonic potential

2006 ◽  
Vol 47 (6) ◽  
pp. 063503 ◽  
Author(s):  
J. Shu ◽  
J. Zhang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Harmonic Potential ◽  
Nonlinear Schrödinger

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

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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