  We apply the theory of infinitesimal transformations for the study of a
family of 1+1 fifth-order partial differential equations which have been
proposed before for the description of multiple kink solutions. In this
analysis we perform a complete classification of the Lie symmetries and of the
one-dimensional optimal system. The results are applied for the derivation of
similarity solutions and in particular we find travel-wave and scaling
solutions. We show that the kink-solution of these equations can be recovered
by the use of the Lie symmetries, while new solutions are also derived.
