关于举行佛山科学技术学院王忠副教授学术报告的通知

报告题目：Stability of the multi-solitons of the modified Korteweg–de Vries equation

报 告人：王忠 副教授 (佛山科学技术学院)

报告时间：2022年4月17日（星期日）上午 10:30-11:30                 

报告地点：腾讯会议，会议号：437-142-433

邀 请人：凌黎明 教授

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数学学院

2022年 4月16日

报告摘要：We establish the nonlinear stability of N-soliton solutions of the modified Korteweg–de Vries (mKdV) equation. The N-soliton solutions are global solutions of mKdV behaving at (positive and negative) time infinity as sums of one-solitons with speeds . The proof relies on the variational characterization of N-solitons. We show that the N-solitons realize the local minimum of the (N + 1)th mKdV conserved quantity subject to fixed constraints on the N first conserved quantities. To this aim, we construct a functional for which N-solitons are critical points, we prove that the spectral properties of the linearization of this functional around an N-soliton are preserved on the extended timeline, and we analyze the spectrum at infinity of linearized operators around one-solitons. The main new ingredients in our analysis are a new operator identity based on a generalized Sylvester law of inertia and recursion operators for the mKdV equation.

报告人简介：王忠，佛山科学技术学院数学系副教授，2016年毕业于中山大学，师从崔尚斌教授；曾先后访问法国巴黎综合理工学院Yvan Martel 和图卢兹第三大学。主要研究方向为非线性色散方程多孤立子解的稳定性和渐近稳定性，并且在CVPDE, Nonlinearity 等期刊发表多篇学术论文，曾主持青年基金和广东省基金等项目。