报告题目：On the stability of solitary waves in the NLS system of the third-harmonic generation in 3D
On the stability of solitary waves in the NLS system of the third-harmonic generation in 2D
报告人：Atanas Stefanov（美国阿拉巴马伯明翰分校教授）
报告时间：2023年5月8日 上午8:00-9:00
2023年5月10日 上午8:00-9:00
腾讯会议号：766-286-298
邀请人：程 星
报告摘要：We consider the NLS system of the third-harmonic generation, which was introduced recently by Sammut et.al. Our interest is in solitary wave solutions and their stability properties. We construct the waves in the largest possible parameter space, and we provide a complete classification of their stability.
In the first talk, we consider the 3 dimensional case. In 3 D case, and for some more restrictive set of parameters, we use virial identities methods to derive the strong instability, in the spirit of M. Ohta's approach.
In the second talk, we consider the 2 dimensional case. In 2D, the virial identities reduce matters, via conservation of mass and energy, to the initial data. Our conclusions mirror closely the well-known results for the scalar cubic focusing NLS, while the proofs are much more involved.
报告人简介：Atanas Stefanov是保加利亚裔美国数学家，现在为美国阿拉巴马大学伯明翰大学的教授。主要从事调和分析、偏微分方程及数学物理等研究方向，目前已经发表学术论文80多篇，例如在著名数学杂志Comm.Math.Phys.和Adv.Math.等发表论文。发表的论文的累积引用次数超过670次。Stefanov教授为60多个重要数学杂志的学术论文进行匿名评审，获得多项美国国家自然科学基金的资助，且在2015年获得堪萨斯大学的学术成就奖。
