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Nanosystems: Physics, Chemistry, Mathematics, 2018, Volume 9, Issue 2, Pages 187–195
DOI: https://doi.org/10.17586/2220-8054-2018-9-2-187-195 (Mi nano151) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

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

R. Carlonea, M. Correggib, L. Tentarellib

a 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
Full-text PDF (243 kB) Citations (1)
DOI: https://doi.org/10.17586/2220-8054-2018-9-2-187-195
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.
Received: 30.01.2018
Revised: 10.02.2018
Bibliographic databases:
Document Type: Article
PACS: 03.65.-w, 02.30.Rz
Language: English
Citation: R. Carlone, M. Correggi, L. Tentarelli, “An introduction to the two-dimensional Schrödinger equation with nonlinear point interactions”, Nanosystems: Physics, Chemistry, Mathematics, 9:2 (2018), 187–195
Citation in format AMSBIB
\Bibitem{CarCorTen18}
\by R.~Carlone, M.~Correggi, L.~Tentarelli
\paper An introduction to the two-dimensional Schr\"odinger equation with nonlinear point interactions
\jour Nanosystems: Physics, Chemistry, Mathematics
\yr 2018
\vol 9
\issue 2
\pages 187--195
\mathnet{http://mi.mathnet.ru/nano151}
\crossref{https://doi.org/10.17586/2220-8054-2018-9-2-187-195}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000431269000005}
\elib{https://elibrary.ru/item.asp?id=32760268}
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    • This publication is cited in the following 1 articles:
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