NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2018, 9 (2), P. 187–195
An introduction to the two-dimensional Schrödinger equation with nonlinear point interactions
R. Carlone – Universitá “Federico II” di Napoli, Dipartimento di Matematica e Applicazioni “R. Caccioppoli” MSA, via Cinthia, I-80126, Napoli, Italy; raffaele.carlone@unina.it
M. Correggi – “Sapienza” Universitá di Roma, Dipartimento di Matematica P.le Aldo Moro, 5, 00185, Roma, Italy; michele.correggi@gmail.com
L. Tentarelli – “Sapienza” Universitá di Roma, Dipartimento di Matematica P.le Aldo Moro, 5, 00185, Roma, Italy; tentarelli@mat.uniroma1.it
We present an introduction to the nonlinear Schrödinger equation (NLSE) with concentrated nonlinearities in R2. 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
DOI 10.17586/2220-8054-2018-9-2-187-195