An introduction to the two-dimensional Schr\"odinger equation with nonlinear point interactions
Mathematical Physics
2022-07-08 v1 Analysis of PDEs
math.MP
Quantum Physics
Abstract
We present an introduction to the nonlinear Schr\"odinger equation (NLSE) with concentrated nonlinearities in . Precisely, taking a cue from the linear problem, we sketch the main challenges and the typical difficulties that arise in the two-dimensional case, and mention some recent results obtained by the authors on local and global well-posedness.
Cite
@article{arxiv.1804.10348,
title = {An introduction to the two-dimensional Schr\"odinger equation with nonlinear point interactions},
author = {R Carlone and M Correggi and L Tentarelli},
journal= {arXiv preprint arXiv:1804.10348},
year = {2022}
}