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arXiv · 2001.03969

Stability of the standing waves of the concentrated NLSE in dimension two

Riccardo Adami·Raffaele Carlone·Michele Correggi·Lorenzo Tentarelli
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Abstract

In this paper we will continue the analysis of two dimensional Schr\"odinger equation with a fixed, pointwise, nonlinearity started in [2, 13]. In this model, the occurrence of a blow-up phenomenon has two peculiar features: the energy threshold under which all solutions blow up is strictly negative and coincides with the infimum of the energy of the standing waves; there is no critical power nonlinearity, i.e., for every power there exist blow-up solutions. Here we study the stability properties of stationary states to verify whether the anomalies mentioned before have any counterpart on the stability features.

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Riccardo Adami, Raffaele Carlone, Michele Correggi, Lorenzo Tentarelli. 2020-01-12. Stability of the standing waves of the concentrated NLSE in dimension two. https://doi.org/10.3934/mine.2021011

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