Abstract
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.
Original language | English |
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Pages (from-to) | 957-981 |
Number of pages | 25 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 67 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2014 Jun |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics