報告題目：Far-Field Behaviors of Multiple-Pole Solitons of the focusing NLS and mKdV equations in the Large-Order Limit
報告時間：2020年11月13日周五14：00—16：00
報告地點：騰訊會議ID：813 521 566
報告人：王燈山 教授
報告摘要：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.
報告人簡介：王燈山，北京師範大學數學科學必一，教授、博士生導師。主要從事可積系統和漸近分析方面的研究，主持國家自然科學基金面上項目等國家級和省部級項目10余項，參與獲得北京市科學技術獎一等獎。入選北京市“科技新星”計劃、北京市“高創計劃”青年拔尖人才和北京市“長城學者”計劃。