Xianguo Geng, Zhengzhou University

Xiangke Chang, Associate Professor

Algebro-geometric solutions to the Bogoyavlensky lattice 2(3) equations

9:50-10:40 December 2(Friday), Tencent Meeting ID: 125-783-025

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.