报告题目：Quasi-periodic solutions of a discrete integrable equation with a finite-dimensional integrable symplectic structure

报告人：赵秋兰教授，山东科技大学

报告时间：2024年11月21日（周四）14:00

报告地点：腾讯会议：848-356-2585

报告摘要：Through the paper, we research the quasi-periodic solutions to a semi-discrete hierarchy which has Hamiltonian structure and integrable symplectic map. Firstly, a semi-discrete hierarchy is derived by use of the discrete zero-curvature representation and then its integrability is proved under the Liouville condition. Using the binary nonlinearization approach, the integrable symplectic map and finite-dimensional Hamiltonian system of the hierarchy are obtained. Moreover, the trigonal curve is denoted through the characteristic polynomials for the Lax pair, as well as the related Baker–Akhiezer function and meromorphic function are introduced, from which the asymptotic properties and divisors of the two functions mentioned above are analyzed. Finally, we introduce the three kinds of Abel differentials and straighten out of corresponding continuous and discrete flows, the quasi-periodic solutions of the equations are received via the Riemann theta function.

报告人简介：赵秋兰，博士，教授，山东科技大学“菁英计划”A类人才计划。目前研究领域为孤子理论、可积系统、数学物理。在Physica D、Chaos等国际主流学术期刊上发表SCI检索研究论文60余篇，主持国家青年基金等各类项目3项。获得过学校“优秀教师”、“我心目中的好老师”等荣誉称号。

邀请人：张翼