najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2015-6-1-79-94najo-916Research ArticleCONTRIBUTED TALKSCONTRIBUTED TALKSOn the derivation of the Schrödinger equation with point-like nonlinearityCacciapuotiC.

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claudio.cacciapuoti@uninsubria.itDipartimento di Scienza e Alta Tecnologia, Universita dell'InsubriaItaly201515082025617994Copyright © Cacciapuoti C., 20252025Cacciapuoti C.Cacciapuoti C.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/916

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.

Nonlinear Schrodinger equationnonlinear delta interactionszero-range limit of concentrated nonlinearitiesThe author is grateful to his friends and collaborators Domenico Finco, Diego Noja, and Alessandro Teta, all the results and conjectures presented in this report were obtained and formulated in collaboration with them. The support of the FIR 2013 project \Condensed Matter in Mathematical Physics" (code RBFR13WAET) is also acknowledged.ReferencesAdami, R., Dell'Antonio, G., Figari, R., and Teta, A., The Cauchy problem for the Schrodinger equation in dimension three with concentrated nonlinearity, Ann. Inst. H. Poincare Anal. Non Lineaire 20 (2003), no. 3, 477{500.Adami, R., Dell'Antonio, G., Figari, R., and Teta, A., The Cauchy problem for the Schrodinger equation in dimension three with concentrated nonlinearity, Ann. Inst. H. Poincare Anal. 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The authors declare that there are no conflicts of interest present.