A Lie algebraic setting for Miura maps related to an energy dependent linear problem

We study the problem of complete parametrization of the moduli space ofSU(2) Yang-Mills-Higgs monopoles in terms of a nonlinear integrable system. It is shown that the moduli space is homeomorphic to the solution space of a new generalization of finite nonperiodic Toda equation called the complex cyclic-Toda hierarchy.