报告题目: The Sylvester equation and the elliptic Korteweg-de Vries system

报告人：孙莹莹

报告时间：2022年4月19号 (周二) 9:30-10:30

报告地点：#腾讯会议： 805-579-131

报告摘要：In my talk I will focus on an elliptic potential Korteweg-de Vries system which is a multi-component extension of the potential Korteweg-de Vries equation. Soliton solutions for this system are associated with an elliptic Cauchy kernel (i.e., a Cauchy kernel on the torus). By using the generalized Cauchy matrix method, we generalize the class of solutions by allowing the spectral parameter to be a full matrix obeying a matrix version of the equation of the elliptic curve, and for the Cauchy matrix to be a solution of a Sylvester type matrix equation subject to this matrix elliptic curve equation. The construction involves solving the matrix elliptic curve equation by using Toeplitz matrix techniques, and analysing the solution of the Sylvester equation in terms of Jordan normal forms. Furthermore, we consider the continuum limit system associated with the elliptic potential Korteweg-de Vries system, and analyse the dynamics of the soliton solutions.

报告人简介：孙莹莹，上海理工大学数学系讲师，硕士生导师。2017年博士毕业于上海大学，悉尼大学博士后，曾访问日本青山学院、澳大利亚弗林德斯大学。主要从事孤立子与可积系统的研究，包括连续与离散可积系统、特殊函数、离散Painlevé方程等。在数学物理领域学术期刊发表SCI论文10余篇。主持国家自然科学基金青年基金项目、上海市扬帆计划等研究课题。

邀请人：赵松林