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Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations (2105.06661v1)

Published 14 May 2021 in nlin.SI, math-ph, math.AP, and math.MP

Abstract: 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.

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