  Studied in this paper is the sixth-order Boussinesq equation. We extend the
local well-posedness theory for this equation with quadratic and cubic
nonlinearities to the high dimensional case. In spite of having the ``bad''
fourth term $\Delta u$ in the equation, we derive some dispersive estimates
leading to the existence of local solutions which also improves the previous
results in the cubic case. In addition, we show persistence of spatial
analyticity of solutions for the cubic nonlinearity.
