  We study solitary-wave and kink-wave solutions of a modified Boussinesq
equation through a multiple-time reductive perturbation method. We use
appropriated modified Korteweg-de Vries hierarchies to eliminate secular
producing terms in each order of the perturbative scheme. We show that the
multiple-time variables needed to obtain a regular perturbative series are
completely determined by the associated linear theory in the case of a
solitary-wave solution, but requires the knowledge of each order of the
perturbative series in the case of a kink-wave solution. These appropriate
multiple-time variables allow us to show that the solitary-wave as well as the
kink-wave solutions of the modified Botussinesq equation are actually
respectively a solitary-wave and a kink-wave satisfying all the equations of
suitable modified Korteweg-de Vries hierarchies.
