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 u t t = u x x + β u x x x x + u x x x x x x + ( u 2 ) x x , where β = ± 1 . We prove the local well-posedness with initial data in non-homogeneous Sobolev spaces H s ( R ) for negative indices of s ∈ R .