Local well-posedness for the sixth-order Boussinesq equation

In this work we study the local well-posedness of the initial value problem for the nonlinear sixth-order Boussinesq equation utt=uxx+βuxxxx+uxxxxxx+(u2)xx, where β=±1. We prove the local well-posedness with initial data in non-homogeneous Sobolev spaces Hs(R) for negative indices of s∈R.