Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations

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