报告题目：Global flows for the cubic nonlinear Schrödinger equation without decay assumptions

报 告 人：Shuo Zhang (张朔, PhD Student@NJU - Nanjing University)

报告时间：2026年11月5日（星期四）9:00—9:45

报告地点：数学科学学院114      

校内联系人：廖娴 教授       联系方式：84708351-8510

Abstract: We study the one-dimensional cubic nonlinear Schrödinger equation on the real line without decay assumptions on the initial data. For both the focusing and defocusing equations, we construct global flows on classes of potentials defined through spectral data, realizing the NLS evolution as a group action. The construction combines Toeplitz operators, associated tau functions, and Weyl functions of Dirac operators. In particular, it yields global classical solutions for arbitrary initial data in (W^{5,\infty}(\mathbb R)), allowing periodic, almost periodic, and more general non-decaying profiles. We also establish global well-posedness in the modulation spaces (M_{\infty,1}^{s}(\mathbb R)) for (s\geq5), and show that spatial Bohr almost periodicity and the associated frequency module are preserved by the flow.

This is joint work with Shinichi Kotani, Yiqian Wang, and Jiahao Xu.