Dimension reduction for Nonlinear Schrödinger equations
Abstract
We discuss mathematical methods to derive Nonlinear Schrödinger equations (NLS) in "low dimensional" settings, i.e. the 3-dimensional physical space e.g. to 2 or 1 space dimensions. Beside from the case the system exhibits an internal symmetry we consider the approaches of dimension reduction via confinement limits and the method of variation. We deal with 2 types of NLS: nonlocal nonlinearities like the Hartree equation, including the Schrödinger--Poisson system (SPS), and local nonlinearities like the Gross--Pitaevskii equation (GPE). Our theoretical considerations of dimension reduction get finally illustrated by numerical examples in a "quasi 1-d" setting.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2023
- DOI:
- arXiv:
- arXiv:2311.01586
- Bibcode:
- 2023arXiv231101586A
- Keywords:
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- Physics - Computational Physics;
- Mathematics - Analysis of PDEs
- E-Print:
- Due to the lack of permission and the inadequately highlighted contribution of the initial co-authors, I hereby withdraw the article. The author was responsible for the execution based on a concept