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.

中文翻译：

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一族 1+1 五阶偏微分方程的李对称性和相似性解

摘要

我们将无穷小变换理论应用于研究一族 1+1 五阶偏微分方程组，这些方程组之前已被提出用于描述多个扭结解。在这个分析中，我们对李对称和一维最优系统进行了完整的分类。结果被应用于相似性解决方案的推导，特别是我们找到了行波和缩放解决方案。我们表明，这些方程的扭结解可以通过使用李对称性来恢复，同时也导出了新的解。