The Gross-Pitaevskii equation in the energy space

2008 ◽  
pp. 129-148 ◽  
Author(s):  
Patrick Gérard
Keyword(s):  
Energy Space ◽  
Pitaevskii Equation

scholarly journals Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation

2014 ◽  
Vol 64 (1) ◽  
pp. 19-70 ◽  
Author(s):  
Fabrice Béthuel ◽  
Philippe Gravejat ◽  
Didier Smets
Keyword(s):  
Energy Space ◽  
Pitaevskii Equation ◽  
One Dimensional ◽  
The One

scholarly journals Almost conservation laws for stochastic nonlinear Schrödinger equations

2021 ◽  
Author(s):  
Kelvin Cheung ◽  
Guopeng Li ◽  
Tadahiro Oh
Keyword(s):  
Conservation Laws ◽  
Stopping Time ◽  
Energy Space ◽  
Stochastic Forcing ◽  
Time Dynamics ◽  
Nonlinear Schrödinger ◽  
Time Argument ◽  
Cubic Nonlinear Schrödinger Equation ◽  
Stochastic Setting ◽  
Ito's Lemma

AbstractIn this paper, we present a globalization argument for stochastic nonlinear dispersive PDEs with additive noises by adapting the I-method (= the method of almost conservation laws) to the stochastic setting. As a model example, we consider the defocusing stochastic cubic nonlinear Schrödinger equation (SNLS) on $${\mathbb {R}}^3$$ R 3 with additive stochastic forcing, white in time and correlated in space, such that the noise lies below the energy space. By combining the I-method with Ito’s lemma and a stopping time argument, we construct global-in-time dynamics for SNLS below the energy space.

scholarly journals Dilute dipolar quantum droplets beyond the extended Gross-Pitaevskii equation

2019 ◽  
Vol 1 (3) ◽  
Author(s):  
Fabian Böttcher ◽  
Matthias Wenzel ◽  
Jan-Niklas Schmidt ◽  
Mingyang Guo ◽  
Tim Langen ◽  
...  
Keyword(s):  
Pitaevskii Equation
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