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arXiv · 1804.10348

An introduction to the two-dimensional Schr\"odinger equation with nonlinear point interactions

R Carlone·M Correggi·L Tentarelli
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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.

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R Carlone, M Correggi, L Tentarelli. 2018-04-27. An introduction to the two-dimensional Schr\"odinger equation with nonlinear point interactions. https://doi.org/10.17586/2220-8054-2018-9-2-187-195

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