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 κ 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. [ABSTRACT FROM AUTHOR]