An introduction to the two-dimensional Schr\"odinger equation with nonlinear point interactions
Nanosistemy: fizika, himiâ, matematika, Tome 9 (2018) no. 2, pp. 187-195
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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.
@article{NANO_2018_9_2_a4,
author = {R. Carlone and M. Correggi and L. Tentarelli},
title = {An introduction to the two-dimensional {Schr\"odinger} equation with nonlinear point interactions},
journal = {Nanosistemy: fizika, himi\^a, matematika},
pages = {187--195},
publisher = {mathdoc},
volume = {9},
number = {2},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/NANO_2018_9_2_a4/}
}
TY - JOUR AU - R. Carlone AU - M. Correggi AU - L. Tentarelli TI - An introduction to the two-dimensional Schr\"odinger equation with nonlinear point interactions JO - Nanosistemy: fizika, himiâ, matematika PY - 2018 SP - 187 EP - 195 VL - 9 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/NANO_2018_9_2_a4/ LA - en ID - NANO_2018_9_2_a4 ER -
%0 Journal Article %A R. Carlone %A M. Correggi %A L. Tentarelli %T An introduction to the two-dimensional Schr\"odinger equation with nonlinear point interactions %J Nanosistemy: fizika, himiâ, matematika %D 2018 %P 187-195 %V 9 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/NANO_2018_9_2_a4/ %G en %F NANO_2018_9_2_a4
R. Carlone; M. Correggi; L. Tentarelli. An introduction to the two-dimensional Schr\"odinger equation with nonlinear point interactions. Nanosistemy: fizika, himiâ, matematika, Tome 9 (2018) no. 2, pp. 187-195. http://geodesic.mathdoc.fr/item/NANO_2018_9_2_a4/