The Prolongation Structures and Nonlocal Symmetries for Modified Boussinesq System

The Wahlquist-Estabrook (WE) prolongation structures of modified Boussinesq (MB) system are studied from the coverings point of view. The realizations and classifications of one-dimensional coverings of this system are obtained completely. Moreover the sufficient and necessary conditions for a vector field to be a nonlocal symmetry of this system are also demonstrated in the WE prolongation structures.