Algebro-geometric solutions to the Manakov hierarchy

Abstract

The Manakov hierarchy associated with a matrix spectral problem is proposed with the aid of Lenard recursion equations. By using the characteristic polynomial of Lax matrix for the Manakov hierarchy, we introduce a trigonal curve of arithmetic genus , from which we construct the related Baker–Akhiezer function, two algebraic functions carrying the data of the divisor and Dubrovin-type equations. Based on the theory of trigonal curves, the explicit theta function representations of the Baker–Akhiezer function, the two algebraic functions, and in particular, that of solutions for the entire Manakov hierarchy are obtained.

Keywords:

• Manakov hierarchy
• algebro-geometric solution
• trigonal curve

AMS Subject Classifications:

• 35Q51
• 35Q55
• 37K10
• 37K20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China (project nos. [11331008], [11171312], [11326163], [11401230]).