Abstract
The mixed Boussinesq hierarchy associated with a 3×3 matrix spectral problem is proposed in view of Lenard recursion equations and the stationary zero-curvature equation. A trigonal curve K m -1 is introduced with the help of the characteristic polynomial of the Lax matrix, from which we construct closely related Baker- Akhiezer function, the meromorphic function and Dubrovin-type equations. Moreover, the flows are straighten out under the Abel map. Based on the basic knowledge of the trigonal curves and three kinds of Abelian differential forms, the Riemann θ function representations of the Baker-Akhiezer function, the meromorphic function, and in particular, that of finite genus solutions for the mixed Boussinesq equation are obtained.
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