Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772310 | Journal of Functional Analysis | 2017 | 48 Pages |
Abstract
We consider a scaling limit of a nonlinear Schrödinger equation (NLS) with a nonlocal nonlinearity showing that it reproduces in the limit of cutoff removal a NLS equation with nonlinearity concentrated at a point. The regularized dynamics is described by the equationiââtÏε(t)=âÎÏε(t)+g(ε,μ,|(Ïε,Ïε(t))|2μ)(Ïε,Ïε(t))Ïε where Ïεâδ0 weakly and the function g embodies the nonlinearity and the scaling and has to be fine tuned in order to have a nontrivial limit dynamics. The limit dynamics is a nonlinear version of point interaction in dimension three and it has been previously studied in several papers as regards the well-posedness, blow-up and asymptotic properties of solutions. Our result is the first justification of the model as the point limit of a regularized dynamics.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Claudio Cacciapuoti, Domenico Finco, Diego Noja, Alessandro Teta,