Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Xianguo Geng，Zhengzhou University
Inviter:	常向科
Title:	Algebro-geometric solutions to the Bogoyavlensky lattice 2(3) equations
Language:	Chinese
Time & Venue:	2022.12.02 09:50-10:40 腾讯会议：125-783-025
Abstract:	The theory of tetragonal curves is established and first applied to the study of algebro-geometric quasi-periodic solutions of discrete soliton equations. Using the zero-curvature equation and the discrete Lenard equation, we derive the hierarchy of Bogoyavlensky lattice 2(3) equations associated with a discrete 4×4 matrix spectral problem. Resorting to the characteristic polynomial of the Lax matrix of this hierarchy, we introduce a tetragonal curve and associated Riemann theta functions and explore the algebro-geometric properties of Baker–Akhiezer functions and a class of meromorphic functions on the tetragonal curve. The straightening out of various flows is precisely given through the Abel map and Abelian differentials. We finally obtain algebro-geometric quasi-periodic solutions of the entire hierarchy of Bogoyavlensky lattice 2(3) equations.