This article is cited in 1 paper

MATHEMATICS

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

R. Carlone^a, M. Correggi^b, L. Tentarelli<sup>b

a</sup> Università "Federico II" di Napoli, Dipartimento di Matematica e Applicazioni "R. Caccioppoli", MSA, via Cinthia, I-80126, Napoli, Italy
^b "Sapienza" Università di Roma, Dipartimento di Matematica P.le Aldo Moro, 5, 00185, Roma, Italy

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.

Keywords: nonlinear Schrödinger equation, nonlinear delta interactions.

PACS: 03.65.-w, 02.30.Rz

Received: 30.01.2018
Revised: 10.02.2018

Language: English

DOI: 10.17586/2220-8054-2018-9-2-187-195

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