Speaker：Xianguo Geng（Zhegnzhou University）

Time：2022-11-22, 09:00

Location：Tencent Meeting ID：466-005-8776（No Password）

Abstract:

On the basis of the characteristic polynomials of Lax matrices for the soliton hierarchies, we introduce the corresponding algebraic curves, including the hyperelliptic curve, trigonal curve, and tetragonal curve. We study the calculations of genuses for these algebraic curves, their properties at infinity, and the construction of three kinds of Abel differentials. We establish the corresponding Baker-Akhiezer functions and meromorphic functions. The straightening out of various soliton flows is exactly given through the Abel map and Abel-Jacobi coordinates. Using the theory of algebraic curves, we obtain the explicit Riemann theta function representations of the Baker-Akhiezer function and the meromorphic function. As an illustration, we arrive at algebro-geometric solutions of the entire Satsuma-Hirota coupled hierarchy.