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

In this paper we will continue the analysis of two dimensional Schrödinger 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.

preprint2020arXivOpen access
Riccardo AdamiRaffaele CarloneMichele CorreggiLorenzo Tentarelli
math.APmath-phmath.MP
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Riccardo AdamiRaffaele CarloneMichele CorreggiLorenzo Tentarelli

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