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 |
|---|---|
| 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
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Cuccagna, S., Visciglia, N., & Georgiev, V. (2014). Decay and scattering of small solutions of pure power NLS in ℝ with p>3 and with a potential. Communications on Pure and Applied Mathematics, 67(6), 957-981. https://doi.org/10.1002/cpa.21465