报告题目：Spectral theory for periodic vector NLS equations

报 告 人：Evgeny Korotyaev 教授（东北师范大学）

报告时间：2025年10月21日（星期二）14:00—15:00

报告地点：数学科学学院114（小报告厅）

校内联系人：胡奕辰 助理教授     联系方式：84708351-8204

报告摘要：We consider a first order operator with a periodic 3x3 matrix potential on the real line. This operator appears in the problem of the periodic vector NLS equation.  The spectrum of the operator covers the real line, it is union of the spectral bands of multiplicity 3, separated by intervals of multiplicity 1. The main results of this work are the following:

1)  The Lyapunov function on the corresponding 2 or 3-sheeted Riemann surface is described.

2) Necessary and sufficient conditions are given when the Riemann surface is 2-sheeted.

3) The asymptotics of 2-periodic eigenvalues are determined.

4)  One constructs an entire function, which is positive on the spectrum of multiplicity 3 and is negative on its gaps.

5)  The estimate of the potential in terms of gap lengths is obtained.

6)  The Borg type results about inverse problems are solved.

7) The solution of the periodic vector NLS equation for the case of the 2-sheeted Riemann surface  is described.。

报告人简介：Evgeny Korotyaev，东北师范大学，前沿交叉研究院教授，圣彼得堡国立大学，数学-力学系教授，俄罗斯高等经济研究大学兼职教授。1982年于圣彼得堡国立大学获PhD学位，1996年于圣彼得堡Steklov研究所获理学博士学位。长期致力于逆谱理论与可积系统、几何函数论、散射理论、薛定谔算子等方向的研究工作，在Invent. Math., Commun. Math. Phys.,Trans. Am. Math. Soc., Inverse Probl., JFA, JDE等期刊发表学术论文150余篇。