  This work studies the local well-posedness of the initial-value problem for
the nonlinear sixth-order Boussinesq equation $u_{tt}=u_{xx}+\beta
u_{xxxx}+u_{xxxxxx}+(u^2)_{xx}$, where $\beta=\pm1$. We prove local
well-posedness with initial data in non-homogeneous Sobolev spaces $H^s(\R)$
for negative indices of $s \in \R$.
