APPLICATION OF THE TRIGONAL CURVE TO THE BLASZAK-MARCINIAK LATTICE HIERARCHY

作者：Geng, Xianguo; Zeng, Xin^*

来源：Theoretical and Mathematical Physics, 2017, 190(1): 18-42.

DOI：10.1134/S0040577917010020

• Blaszak-Marciniak lattice
• algebro-geometric solution
• trigonal curve

We develop a method for constructing algebro-geometric solutions of the Blaszak-Marciniak (BM) lattice hierarchy based on the theory of trigonal curves. We first derive the BM lattice hierarchy associated with a discrete (3x3)-matrix spectral problem using Lenard recurrence relations. Using the characteristic polynomial of the Lax matrix for the BM lattice hierarchy, we introduce a trigonal curve with two infinite points, which we use to establish the associated Dubrovin-type equations. We then study the asymptotic properties of the algebraic function carrying the data of the divisor and the Baker-Akhiezer function near the two infinite points on the trigonal curve. We finally obtain algebro-geometric solutions of the entire BM lattice hierarchy in terms of the Riemann theta function.

• 出版日期2017-1
• 单位郑州大学