可积系统系列报告-Stability of elliptic function solutions for the focusing modified KdV equation

讲座题目Title：可积系统系列报告-Stability of elliptic function solutions for the focusing modified KdV equation

讲座时间 Datetime: 2023年 11月01日  14:30—17:00

地点 Venue: 中大珠海校区海琴二号A455

报告人 Speaker: 凌黎明 教授

单位 Affiliation: 华南理工大学

主持人Host：吴志伟 副教授

报告摘要 Abstract:

In this talk, we would like to introduce the spectral and orbital stability of elliptic function solutions for the focusing modified KdV equation. The elliptic function solutions of the mKdV equation and related fundamental solutions of the Lax pair are exactly represented by theta functions. Based on the ‘modified squared wavefunction’ method, we construct all linear independent solutions of the linearized mKdV equation and then provide a necessary and sufficient condition of the spectral stability for elliptic function solutions with respect to subharmonic perturbations. In the case of spectrum stability, the orbital stability of elliptic function solutionsis established in a suitable Hilbert space.

报告人简介：

凌黎明，华南理工大学教授，博士生导师。长期从事非线性可积系统的研究，在本领域内发表SCI 论文 50余篇，其中包括 Duke Mathematical Journal， Physical Review E ，Physica D, Studies in Applied Mathematics, Nonlinearity 等杂志，合作出版怪波专著一部。已发表文章在 Google 学术搜索统计引用 3500 余次，其中单篇最高引用 800 次，4篇论文入选ESI高被引论文。先后主持国家自然科学基金项目3项。目前任杂志 Physica D 的青年编辑。