Failure of scattering for the NLSE with a point interaction in dimension two and three

Abstract In this paper we consider the nonlinear Schrödinger (NLS) equation with power nonlinearity and a point interaction (a ‘ δ -potential’ in physical literature) dimension two three. We will show that for low nonlinearities there is failure of scattering to free dynamics or standing waves. recent paper, Murphy Nakanishi (2021 Discrete Contin. Dyn. Syst. 41 1507–17) NLS potentials measures, singular enough include -potential one they analogous properties. extend result higher dimensions needs different treatment linear part interaction, due qualitatively stronger character singularity involved.