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

Abstract

We apply the theory of innitesimal transformations for the study of a family of 1+1 fth-order partial dierential equations which have been proposed before for the description of multiple kink solutions. In this analysis we perform a complete classication 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 nd 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.