报告时间：2024年1月8日下午3:00开始
报 告 人：Maksim Pavlov（俄罗斯科学院列别捷夫物理研究所 研究员）
报告地点：包玉书9号楼305
报告题目：Various Solutions of the KdV equation
报告摘要：We consider linear ordinary differential equation of second order, which is a first part of the Lax pair for the KdV equation. Here we discuss the so-called class of "reflectionless" potentials. This case first was investigated by French mathematician Jules Drach in 1919. Later (1975) these equations were independently derived by B.A. Dubrovin for the KdV equation. In the talk we discuss two special cases: multi-soliton solutions and elliptic solutions (Lame potentials). Beyond reflectionless potentials, the following examples of open problems will be given: Airy function, Harmonic oscillator, Painleve 1, Painleve 2 (isomonodromic deformations); Riemann surfaces and algebro-geometric (multi-phase) solutions, other integrable systems and their particular solutions; Commuting differential operators; zero curvature conditions; resolvent equations.
报告人简介：Pavlov研究员系国际数学物理学界著名学者。早年毕业于俄罗斯科学院列别捷夫物理研究所，在国际著名数学家S. P. Novikov教授（菲尔兹奖获得者）的指导下获博士学位。之后在列别捷夫物理研究所任研究员。曾被邀请在国际上很多大学做邀请报告。他主要从事可积系统的哈密顿结构、达布变换和无色散可积系统等方面的研究，发表了多篇在国际上有影响的工作，成果被国际同行普遍引用超过 1 千余次。他被邀请在数学物理领域的多个重要国际会议上做大会报告。
