PAINLEVÉ XXXIV ASYMPTOTICS FOR THE DEFOCUSING NONLINEAR SCHRÖDINGER EQUATION WITH A FINITE-GENUS ALGEBRO-GEOMETRIC BACKGROUND
数学专题报告
报告题目(Title)：PAINLEVÉ XXXIV ASYMPTOTICS FOR THE DEFOCUSING NONLINEAR SCHRÖDINGER EQUATION WITH A FINITE-GENUS ALGEBRO-GEOMETRIC BACKGROUND
报告人(Speaker)：杨依灵 副教授（重庆大学数学与统计学院）
地点(Place)：后主楼1220
时间(Time)：2025年9月28日(周日) 15:00-16:00
邀请人(Inviter)：王灯山
报告摘要
In this paper, we consider the Cauchy problem for the defocusing nonlinear Schrodinger equation with a finite genus algebro-geometric background. Long-time asymptotics of the solution are derived in four space-time regions. It comes out that the leading-order term in the expansion is, up to a constant, given by the background solution with a shift of the parameter. The subleading term, however, decays at different rates for different regions. We particularly highlight that in the two transition regions, they are of order O(t^{−1/3}) and the coefficients involve an integral of the Painlevé XXXIV transcendent. We establish our results by applying a nonlinear steepest descent analysis to the associated Riemann-Hilbert problems
主讲人简介
杨依灵，重庆大学数学与统计学院副教授。2013年进入复旦大学，先后在复旦大学进行本科、硕博及博士后阶段的学习，导师为范恩贵教授。主要利用黎曼-希尔伯特方法研究可积偏微分方程柯西问题解的长时间渐近性与稳定性。目前已在高水平期刊《Adv. Math.》，《J. Lond. Math. Soc.》，《Math. Z.》，《J. Differential Equations》，《Sci. China Math.》等发表论文13篇。主持国家自然科学基金青年项目C类、国家自然科学基金理论物理专项，以及重庆市自然科学基金面上项目、博士后面上资助等省部级项目4项。
