报告题目 Spectral invariants for vector periodic NLS
报告人：Evgeny Korotyaev
所在单位：东北师范大学 交叉学科高级研究院
报告时间：2025年 5月22日 星期四 下午 2：00-3：00
报告地点：数学楼第一报告厅
报告摘要 Firstly, we consider the various properties of periodic Zkharov-Shabat operator,
associated with scaler periodic NLS. We discuss the main results and techniques.
Secondly, we discuss first order operators with a periodic 3x3 matrix potential on the real
line. This operator is the Lax operator for the periodic vector NLS equation. The spectrum
of the operator covers the real line and it is union of the spectrum of multiplicity 3, separated
by intervals (gaps) of multiplicity 1. We prove the following:
· The corresponding 2 or 3-sheeted Riemann surface is described.
· Necessary and sufficient conditions are given when the Riemann surface is 2-sheeted.
In the case of the 2-sheeted Riemann surface the solution of vector NLS equation is determined
in terms of solutions of scalar NLS equations.
· The asymptotics of 2-periodic eigenvalues are determined.
· One constructs an entire function, which is negative on the spectrum of multiplicity 3 and
is positive on its gaps.
报告人简介：Evgeny Korotyaev东北师范大学交叉学科高级研究院特聘教授，研究方向为偏微分方程谱理论，在《SIAM Journal on Mathematical Analysis》等高水平期刊发表论文160余篇。
