報告人：張永帥 副教授
報告題目：Determinant representation of the vector NLS equation with zero boundary condition
報告時間：2026年5月23日（周六）下午14：00
報告地點：騰訊會議：319-508-298
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
張永帥、紹興大學數理信息學院數學系副教授，碩士生導師。2017年畢業于中國科學技術大學數學物理專業。主要研究方向為可積系統及其應用。先后主持國家自然科學基金項目2項（青年項目和面上項目各1項）。已在Nonlinearity、Inverse Problems, Stud. Appl. Math., J. Math. Phys.等發表SCI論文40余篇。入選浙江省領軍人才計劃。
報告摘要：
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.