Algebro-geometric solutions of the modified Jaulent–Miodek hierarchy

Abstract

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 [Formula: see text] and a Riemann surface [Formula: see text] with arithmetic genus [Formula: see text] 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.