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Decay and Scattering of Small Solutions of Pure Power NLS in ℝ with p > 3 and with a Potential
Author(s) -
Cuccagna Scipio,
Visciglia Nicola,
Georgiev Vladimir
Publication year - 2014
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21465
Subject(s) - mathematics , bounded function , nonlinear system , linearization , scattering , exponent , mathematical analysis , invariant (physics) , geodetic datum , exponential function , mathematical physics , quantum mechanics , physics , linguistics , philosophy , cartography , geography
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. © 2014 Wiley Periodicals, Inc.
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