A Collective Coordinate Approach to the One-Dimensional Nonlinear Schrödinger Equation with Spatial Periodic Potentials

1993 ◽  
pp. 85-96
Author(s):  
A. R. Bishop ◽  
Rainer Scharf
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
One Dimensional ◽  
Nonlinear Schrödinger ◽  
Periodic Potentials ◽  
Collective Coordinate ◽  
The One

scholarly journals STOCHASTIC NONLINEAR SCHRÖDINGER EQUATION WITH ALMOST SPACE–TIME WHITE NOISE

2019 ◽  
Vol 109 (1) ◽  
pp. 44-67 ◽  
Author(s):  
JUSTIN FORLANO ◽  
TADAHIRO OH ◽  
YUZHAO WANG
Keyword(s):  
Schrödinger Equation ◽  
White Noise ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Space Time ◽  
Nonlinear Schrodinger Equation ◽  
One Dimensional ◽  
Nonlinear Schrödinger ◽  
The One ◽  
Cubic Nonlinear Schrödinger Equation

We study the stochastic cubic nonlinear Schrödinger equation (SNLS) with an additive noise on the one-dimensional torus. In particular, we prove local well-posedness of the (renormalized) SNLS when the noise is almost space–time white noise. We also discuss a notion of criticality in this stochastic context, comparing the situation with the stochastic cubic heat equation (also known as the stochastic quantization equation).

scholarly journals Dynamics of solitons in the one-dimensional nonlinear Schrödinger equation

2016 ◽  
Vol 70 (11) ◽  
Author(s):  
Tobias Ilg ◽  
Ramona Tschüter ◽  
Andrej Junginger ◽  
Jörg Main ◽  
Günter Wunner
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
One Dimensional ◽  
Nonlinear Schrödinger ◽  
The One
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