Algebro-geometric solutions of the generalized Burgers hierarchy associated with a 3 × 3 matrix spectral problem based on Riemann surface

Abstract

Abstract A generalized Burgers hierarchy associated with the 3 × 3 matrix spectral problem is presented with the aid of Lenard recursion equations and the zero-curvature equation. Based on the characteristic polynomial of Lax matrix for the hierarchy, a third order algebraic curve K m − 1 with genus m − 1 is introduced, on which we establish the associated meromorphic function, Baker–Akhiezer functions and Dubrovin-type equations. Furthermore, the Abel map is introduced to straighten out the corresponding flows. Finally, by employing the property of the meromorphic function and Baker–Akhiezer function and their asymptotic expansions, we derive their explicit Riemann theta function representations. From which algebro-geometric solutions for the whole hierarchy are obtained.