多孤子解的1维次临界NLS方程的渐近稳定性
偏微分方程分析
2025-11-13 v3 数学物理
math.MP
摘要
考虑一维次临界非线性薛定谔方程 \begin{equation} i\partial_{t}\psi+\partial^{2}_{x}\psi+\vert \psi\vert^{2k}\psi=0 \text{, }. \end{equation} 众所周知，该方程的孤立波解不稳定。在Krieger和Schlag的开创性工作中，已在codimension-1中心-稳定流形上建立了孤立波解的渐近稳定性。在本文中，我们利用前期工作中用于一维矩阵电荷传递模型的线性估计，\cite{dispanalysis1}，证明了对于，多孤子解在有限codimension流形上的渐近稳定性。
引用
@article{arxiv.2509.03637,
title = {Asymptotic Stability of multi-solitons for $1$d Supercritical NLS},
author = {Gong Chen and Abdon Moutinho},
journal= {arXiv preprint arXiv:2509.03637},
year = {2025}
}
备注
Version 3: REMOVAL OF SOME HYPOTHESES, REMOVAL OF CONDITION OF SEPARATION ON SPEEDS, IMPROVED ESTIMATES FOR THE MODIFIED SCATTERING WAVE OPERATOR OF THE REMAINDER. 82 pages. Keywords: Scattering,, Asymptotic Stability on $H^{1}$ norm, 1d supercritical NLS, multi-solitons, non-integrable, H1 norm, Center-stable Manifold; Mistype errors corrected; Comments are welcome