Geodesic
On the derivation of the Schr\"odinger equation with point-like nonlinearity
Nanosistemy: fizika, himiâ, matematika, Tome 6 (2015) no. 1, pp. 79-94.

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In this report we discuss the problem of approximating nonlinear delta-interactions in dimensions one and three with regular, local or non-local nonlinearities. Concerning the one dimensional case, we discuss a recent result proved in [10], on the derivation of nonlinear delta-interactions as limit of scaled, local nonlinearities. For the three dimensional case, we consider an equation with scaled, non-local nonlinearity. We conjecture that such an equation approximates the nonlinear delta-interaction, and give an heuristic argument to support our conjecture.
Keywords: Nonlinear Schrödinger equation, nonlinear delta interactions, zero-range limit of concentrated nonlinearities. 
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     author = {C. Cacciapuoti},
     title = {On the derivation of the {Schr\"odinger} equation with point-like nonlinearity},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
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C. Cacciapuoti. On the derivation of the Schr\"odinger equation with point-like nonlinearity. Nanosistemy: fizika, himiâ, matematika, Tome 6 (2015) no. 1, pp. 79-94. http://geodesic.mathdoc.fr/item/NANO_2015_6_1_a4/