  We consider the discrete Boussinesq integrable system and the compatible set
of differential difference, and partial differential equations. The latter not
only encode the complete hierarchy of the Boussisesq equation, but also
incorporate the hyperbolic Ernst equations for an Einstein-Maxwell-Weyl field
in general relativity. We demonstrate a specific symmetry reduction of the
partial differential equations, to a six-parameter, second order coupled system
of ordinary differential equations, which is conjectured to be of Garnier type.
