English

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 R2\mathbb{R}^2. 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.

Keywords

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}
}
R2 v1 2026-06-23T01:37:41.381Z