We consider the 1D nonlinear Schrödinger equation with focusing point nonlinearity. "Point"means that the pure-power nonlinearity has an inhomogeneous potential and the potential is the delta function supported at the origin. This equation is used to model a Kerr-type medium with a narrow strip in the optic fibre. There are several mathematical studies on this equation and the local/global existence of a solution, blow-up occurrence, and blowup profile have been investigated. In this paper we focus on the asymptotic behavior of the global solution, i.e., we show that the global solution scatters as t → ±∞ in the L2 supercritical case. The main argument we use is due to Kenig-Merle, but it is required to make use of an appropriate function space (not Strichartz space) according to the smoothing properties of the associated integral equation.
Scattering for the L2supercritical point NLS / Adami, R.; Fukuizumi, R.; Holmer, J.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 374:1(2020), pp. 35-60. [10.1090/tran/8065]
Titolo: | Scattering for the L2supercritical point NLS | |
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Data di pubblicazione: | 2020 | |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1090/tran/8065 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11583/2875545