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

Abstract

We present an introduction to the nonlinear Schrödinger 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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