Decay and Scattering of Small Solutions of Pure Power NLS in ℝ with p > 3 and with a Potential
Decay and Scattering of Small Solutions of Pure Power NLS in ℝ with p > 3 and with a Potential
复制标题
ℝ 中 p > 3 且具有势的纯幂 NLS 小解的衰变和散射
DOI：
10.1002/cpa.21465
复制
发表时间：
2012
影响因子：
3
通讯作者：
V. Georgiev
中科院分区：
文献类型：
--
作者：
S. Cuccagna;N. Visciglia;V. Georgiev
本文证明了当初始数据在有界能量和方差（有界能量和有界方差）中很小时，具有指数为3 < p < 5的纯幂非线性项的非线性薛定谔方程（NLS）解的衰减和散射，其中线性不均匀性由一个真实的值施瓦茨函数的线性势表示.我们假设不存在离散模式。这个证明类似于平移不变方程的证明。特别是，我们找到适当的运营商交换的线性化。© 2014 Wiley Periodicals，Inc.
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.