Algebro-geometric solutions of the modified Jaulent-Miodek hierarchy

According to the polynomial recursion formalism, the modified Jaulent-Miodek hierarchy is derived in a standard way. The first two nontrivial members in the modified Jaulent-Miodek hierarchy are listed correspondingly. Based on the squared eigenfunctions, an algebraic curve ?n and a Riemann surface S with arithmetic genus n are introduced, then the Dubrovin-type equations are obtained naturally. With the help of the conservation laws, the Baker-Akhiezer functions are defined. Finally, the asymptotic properties of the Baker-Akhiezer functions are analyzed, from which the algebro-geometric solutions of the modified Jaulent-Miodek hierarchy are constructed in term of the Riemann theta function.