抄録
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.
| 元の言語 | English |
|---|---|
| ページ（範囲） | 957-981 |
| ページ数 | 25 |
| ジャーナル | Communications on Pure and Applied Mathematics |
| 巻 | 67 |
| 発行部数 | 6 |
| DOI | |
| 出版物ステータス | Published - 2014 |
| 外部発表 | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
これを引用
Decay and scattering of small solutions of pure power NLS in ℝ with p>3 and with a potential. / Cuccagna, Scipio; Visciglia, Nicola; Gueorguiev, Vladimir Simeonov.
：: Communications on Pure and Applied Mathematics, 巻 67, 番号 6, 2014, p. 957-981.研究成果: Article
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TY - JOUR
T1 - Decay and scattering of small solutions of pure power NLS in ℝ with p>3 and with a potential
AU - Cuccagna, Scipio
AU - Visciglia, Nicola
AU - Gueorguiev, Vladimir Simeonov
PY - 2014
Y1 - 2014
N2 - We prove decay and scattering of solutions of the nonlinear Schrödinger equation (NLS) in ℝ with pure power nonlinearity with exponent 3
AB - We prove decay and scattering of solutions of the nonlinear Schrödinger equation (NLS) in ℝ with pure power nonlinearity with exponent 3
UR - http://www.scopus.com/inward/record.url?scp=84896490970&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84896490970&partnerID=8YFLogxK
U2 - 10.1002/cpa.21465
DO - 10.1002/cpa.21465
M3 - Article
AN - SCOPUS:84896490970
VL - 67
SP - 957
EP - 981
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
SN - 0010-3640
IS - 6
ER -