报告人：张永帅 副教授
报告题目：Determinant representation of the vector NLS equation with zero boundary condition
报告时间：2026年5月23日（周六）下午14：00
报告地点：腾讯会议：319-508-298
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
张永帅、绍兴大学数理信息学院数学系副教授，硕士生导师。2017年毕业于中国科学技术大学数学物理专业。主要研究方向为可积系统及其应用。先后主持国家自然科学基金项目2项（青年项目和面上项目各1项）。已在Nonlinearity、Inverse Problems, Stud. Appl. Math., J. Math. Phys. 等发表SCI论文40余篇。入选浙江省领军人才计划。
报告摘要：
In this talk, we investigate the $n$--component nonlinear Schr\{o}dinger (NLS) equation with vanishing boundary conditions within the framework of the Riemann--Hilbert approach. We focus on the spectral problem associated with scattering coefficients that admit zeros of arbitrary order, and subsequently construct the corresponding multiple higher--order pole solitons. Using the dressing matrix method, we transform the singular Riemann--Hilbert problem into a regular one by resolving the singularities induced by these zeros, and derive explicit determinant representations for both higher--order pole solitons and multiple higher--order pole solitons. Through rigorous analysis, we express the entries of the resulting matrices in terms of differential operators and cast these matrices into the Gram determinant form. Leveraging the fundamental properties of the Gram determinant, we establish the regularity of these higher--order pole solitons, including the case of multiple higher--order poles. In addition, we analyze the collision dynamics of second-- and third--order pole soliton solutions. Our results demonstrate that while energy redistribution occurs among the components during soliton collisions, the total energy of the system remains strictly conserved.
