Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	耿献国教授，郑州大学
Inviter:
Title:	The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices
Time & Venue:	2018.12.19 20:00-21:00 N702
Abstract:	Starting with a discrete 3×3 matrix spectral problem, the hierarchy of Bogoyavlensky lattices which are pure differential-difference equations are derived with the aid of the Lenard recursion equations and the stationary discrete zero-curvature equation. By using the characteristic polynomial of Lax matrix for the hierarchy of stationary Bogoyavlensky lattices, we introduce a trigonal curve of arithmetic genus m?1 and a basis of holomorphic differentials on it, from which we construct the Riemann theta function of the trigonal curve, the related Baker-Akhiezer function, and an algebraic function carrying the data of the divisor. Based on the theory of trigonal curves, the Riemann theta function representations of the Baker-Akhiezer function, the meromorphic function, and in particular, that of solutions of the hierarchy of Bogoyavlensky lattices are obtained.