  We determine exact and analytic solutions of the gravitational field
equations in Einstein-aether scalar model field with a Bianchi I background
space. In particular, we consider nonlinear interactions of the scalar field
with the aether field. For the model under consideration we can write the field
equations by using the minisuperspace description. The point-like Lagrangian of
the field equations depends on three unknown functions. We derive conservation
laws for the field equations for specific forms of the unknown functions such
that the field equations are Liouville integrable. Furthermore, we study the
evolution of the field equations and the evolution of the anisotropies by
determining the equilibrium points and analyzing their stability.
