报告题目：A New Integrable Multi-particle McMillan Map and Its Exact Solutions

报告人：周汝光, 江苏师范大学

报告时间：5月8日，2:30-4:00

报告地点：二教2402

摘要：

The classical McMillan map and the Danilov-Nagaitsev model serve as fundamental nonlinear lattice models in accelerator physics, providing the mathematical principles for Nonlinear Integrable Optics. These concepts are currently being validated at Fermilab's Integrable Optics Test Accelerator (IOTA), where McMillan-type potentials are utilized to maintain particle stability and mitigate beam loss across distinct physical regimes. Building upon this physical foundation, we introduce a novel integrable N-particle McMillan map that uniquely accommodates non-identical particles through the inclusion of distinct parameters. The Liouville integrability of this generalized model is rigorously established via a discrete Lax representation and the classical r-matrix method, revealing an explicit structural connection between this discrete symplectic map and the continuous Kaup-Newell hierarchy. Based on this unified spectral framework, we successfully derive exact algebro-geometric solutions for the multi-particle orbits, expressing the discrete dynamical variables explicitly in terms of Riemann theta functions.

报告人简介：

周汝光，江苏师范大学数学与统计学院教授、博士生导师，曾任江苏师范大学校长，现任教育部高等学校数学类专业教学指导委员会委员。1997年在复旦大学获得基础数学方向理学博士学位，长期从事可积系统的数学理论研究，博士论文被评为2000年全国优秀博士学位论文。2001—2002年在德国帕德博恩大学担任洪堡学者。曾参与国家攀登计划“非线性科学”项目及国家重点基础研究发展规划项目“非线性科学中的若干前沿问题”项目各1项，主持完成国家自然科学基金项目6项。入选教育部“新世纪优秀人才支持计划”。研究成果获教育部自然科学二等奖。