报告题目：Far-Field Behaviors of Multiple-Pole Solitons of the focusing NLS and mKdV equations in the Large-Order Limit
报告时间：2020年11月13日周五14：00—16：00
报告地点：腾讯会议ID：813 521 566
报告人：王灯山 教授
报告摘要：The integrable focusing NLS 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. It is shown that in an appropriate scaling, there are four regions in the space-time plane: 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, respectively. This is a joint work with D. Bilman and R. Buckingham [arXiv:1911.04327v1]. Finally, we briefly introduce our recent work on the multiple-pole solitons in the focusing mKdV equation.
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。