学术报告20251209：High genus KdV soliton gases and their long-time asymptotics

报告题目：High genus KdV soliton gases and their long-time asymptotics

报告人：王灯山 教授

报告摘要：In this talk, we report our recent work on the genus two KdV soliton gases and their long-time asymptotics. This work employs the Riemann-Hilbert problem to provide a comprehensive analysis of the asymptotic behavior of the high-genus KdV soliton gases. It is demonstrated that the two-genus soliton gas is related to the two-phase Riemann-Theta function as x→+∞, and approaches to zero as x→−∞. Additionally, the long-time asymptotic behavior of this two-genus soliton gas can be categorized into five distinct regions in the x-t plane, which from left to right are rapidly decay, modulated one-phase wave, unmodulated one-phase wave, modulated two-phase wave, and unmodulated two-phase wave. Moreover, an innovative method is introduced to solve the model problem associated with the high-genus Riemann surface, leading to the determination of the leading terms, which is also related with the multi-phase Riemann-Theta function. A general discussion on the case of arbitrary N-genus soliton gas is also presented. This is a joint work with Dinghao Zhu and Xiaodong Zhu.

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，在Analysis & PDE, Physical Review Letters和Nonlinearity和J. Differential Equations等国际期刊上发表学术论文100余篇，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。入选北京市“科技新星”计划、北京市“高创计划”青年拔尖人才、北京市“长城学者”计划、科睿唯安2025年高被引科学家以及爱思唯尔2020-2024年中国高被引学者。

报告时间：2025年12月9日17：00—18：00

报告地点：数学科学学院512会议室

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内蒙古大学数学科学学院

2025年12月5日