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Far-Field Asymptotics for Multiple-Pole Solitons in the Large-Order Limit

王灯山 教授(北京师范大学)
Thursday, July 16th, 2020, 3:00 PM  腾讯会议(会议 ID:355 863 637)
 
*主持人:陈勇 教授
*时间:2020年7月16日 15:00-16:00
*地点:腾讯会议(会议 ID:355 863 637)

*主讲人简介:
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。

*讲座内容简介:
The integrable focusing nonlinear Schr?dinger 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].
   
 
 
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