Jacobi inversion problem for the modified Jaulent-Miodek hierarchy

The r-matrices and classica1 Poisson structures are constructed for x
⁻
and t
n
⁻
constrained flows of the modified Jaulent-Miodek (MJM) hierarchy. The Lax matrix is used to study the separation of variables method for these constrained through flows. The Jacobi inversion problem for the MJM equation is obtained through the factorization of the MJM equation and the separability of the constrained flows. This is analogous to separation of variables for solving the MJM equation