可积系统系列报告：四方曲线与Blaszak-Marciniak方程族的代数几何解

讲座时间 Datetime: 2021年9月7日 ，星期二，15:00-16:30

地点 Venue: 腾讯会议，518 357 5871

报告人 Speaker:  耿献国 教授

单位 Affiliation: 郑州大学

报告摘要 Abstract:

The theory of tetragonal curves is first applied to the study of discrete integrable systems. Based on the discrete Lenard equation, we derive a hierarchy of Blaszak-Marciniak 4-field lattice equation associated with the  4×4  matrix spectral problem. Resorting to the characteristic polynomial of the Lax matrix for the hierarchy of Blaszak-Marciniak 4-field lattice equation, we introduce a tetragonal curve, a Baker-Akhiezer function, and three meromorphic functions on it. We study algebro-geometric properties of the tetragonal curve and asymptotic behaviors of the Baker-Akhiezer function and meromorphic functions near two infinite points. The straightening out of various flows is exactly given by means of the Abel map and the meromorphic differential. We finally obtain Riemann theta function solutions of the entire Blaszak-Marciniak 4-field lattice hierarchy.