中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
偏微分方程研讨班
Speaker: 廖娴（大连理工大学）
Inviter: 樊洁
Language: Chinese
Title: One-Dimensional Defocusing Cubic Nonlinear Schr\"odinger Equation and Its Hydrodynamic Formulation
Time & Venue: 2026年6月16日（星期二）15：00-16：00 腾讯会议号：965-563-824
Abstract: In this talk, we consider the one-dimensional defocusing cubic nonlinear Schrödinger equation (NLS) and its hydrodynamic formulation (hNLS) obtained through the Madelung transform. We first present the functional framework of the Madelung transform, which allows the global well-posedness theory for (NLS) with nonzero boundary conditions to be transferred to (hNLS) in Sobolev spaces. We then study the associated Lax-pair formulation and construct a unitary transformation that maps the Lax pair (LP) to its hydrodynamic counterpart (hLP). The resulting hydrodynamic Lax operator is a one-dimensional Dirac operator, whose eigenvalues are subsequently analyzed.
附件：