We prove decay and scattering of solutions of the nonlinear Schrödinger equation (NLS) in ℝ with pure power nonlinearity with exponent 3<p<5 when the initial datum is small in Σ (bounded energy and variance) in the presence of a linear inhomogeneity represented by a linear potential that is a real-valued Schwarz function. We assume absence of discrete modes. The proof is analogous to the one for the translation-invariant equation. In particular, we find appropriate operators commuting with the linearization.
|Autori:||S., Cuccagna; Gueorguiev, VLADIMIR SIMEONOV; Visciglia, Nicola|
|Titolo:||Decay and Scattering of Small Solutions of Pure Power NLS in R with p > 3 and with a Potential|
|Anno del prodotto:||2014|
|Digital Object Identifier (DOI):||10.1002/cpa.21465|
|Appare nelle tipologie:||1.1 Articolo in rivista|