讲座题目👉🏻：Far-Field Asymptotics for Multiple-Pole Solitons in the Large-Order Limit 主讲人🤢：王灯山 教授 主持人：陈勇 开始时间：2020-07-16 15:00:00 结束时间🕵🏼♀️：2020-07-16 16:00:00 讲座地址⛹🏿♀️：腾讯会议 (会议 ID：355 863 637) 主办单位：数学科学学院
报告人简介♌️： 王灯山，北京师范大学数学科学学院🧑🏻🦯，教授、博士生导师🧙🏽♂️。主要从事可积系统和渐近分析方面的研究，主持国家自然科学基金面上项目等国家级和省部级项目10余项🪰，参与获得北京市科学技术奖一等奖🫵🏽👎🏽。入选北京市“科技新星”计划、北京市“高创计划”青年拔尖人才和北京市“长城学者”计划。 报告内容： The integrable focusing nonlinear Schrödinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by Darboux transformations as the pole order tends to infinity. We show that in an appropriate scaling, there are four regions in the space-time plane where solutions display qualitatively distinct behaviors: an exponential-decay region, an algebraic-decay region, a non-oscillatory region, and an oscillatory region. Using the nonlinear steepest-descent method for analyzing Riemann-Hilbert problems, we compute the leading-order asymptotic behavior in the algebraic-decay, non-oscillatory, and oscillatory regions.This is a joint work with D. Bilman and R. Buckingham [arXiv:1911.04327v1]. |
