## An introduction to the two-dimensional Schrödinger equation with nonlinear point interactions

created by tentarelli on 08 Jul 2022

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Published Paper

Inserted: 8 jul 2022
Last Updated: 8 jul 2022

Journal: Nanosystems: Phys. Chem. Math.
Volume: 9
Number: 2
Pages: 187-195
Year: 2018
Doi: 10.17586/2220-8054-2018-9-2-187-195

ArXiv: 1804.10348 PDF

Abstract:

We present an introduction to the nonlinear Schr\"odinger equation (NLSE) with concentrated nonlinearities in $\mathbb{R}^2$. 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.