Quasi-periodic solutions of three-component Burgers hierarchy

Abstract

Starting from a $ 3\times3 $ matrix spectral problem and the characteristic polynomial of the Lax matrix, we propose a trigonal curve, the associated meromorphic functions and three kinds of Abelian differentials. By discussing the asymptotic properties for the Baker-Akhiezer functions and their Riemann theta function expressions, we get quasi-periodic solutions of the three-component Burgers hierarchy. Finally, we straighten out the three-component Burgers flows.

Keywords

• three-component burgers hierarchy
• quasi-periodic solutions
• baker-akhiezer function
• trigonal curve