Solution of the one-dimensional spatially inhomogeneous cubic-quintic nonlinear Schrödinger equation with an external potential

2007 ◽  
Vol 76 (1) ◽  
Author(s):  
Xiao-Yan Tang ◽  
Padma Kant Shukla
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
External Potential ◽  
One Dimensional ◽  
Nonlinear Schrödinger ◽  
Spatially Inhomogeneous ◽  
The One ◽  
Quintic Nonlinear Schrödinger Equation

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).

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