A hierarchy of generalized Jaulent-Miodek equations and their explicit solutions

A hierarchy of generalized Jaulent-Miodek (JM) equations related to a new spectral problem with energy-dependent potentials is proposed. Depending on the Lax matrix and elliptic variables, the generalized JM hierarchy is decomposed into two systems of solvable ordinary differential equations. Explicit theta function representations of the meromorphic function and the Baker-Akhiezer function are constructed, the solutions of the hierarchy are obtained based on the theory of algebraic curves.