Geodesic
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. 
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     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},
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     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2018_9_2_a4/}
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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/