The paper investigates a class of long-wave unstable lubrication model using Lie theory. A nonlinear self-adjoint classification of the considered equation is carried out. Without having to go into microscopic details of the physical aspects, non-trivial conservation laws are computed. Then, minimal set of Lie point symmetries of the discussed model is classified up to one-dimensional conjugacy classes which are further utilised one by one to construct the similarity variables to reduce the dimension of the considered model. After that, all possible phase trajectories are classified with respect to the parameters of the equation. Some travelling wave and kink-wave solutions are also showed and graphical representations are displayed to depict their propagation.

中文翻译：

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一类长波不稳定润滑模型的非线性自邻接、守恒量、分岔分析及行波解

本文利用李理论研究了一类长波不稳定润滑模型。对所考虑的方程进行非线性自伴随分类。无需深入研究物理方面的微观细节，即可计算非平凡守恒定律。然后，将所讨论模型的最小李点对称集分类为一维共轭类，这些共轭类进一步被一一利用以构建相似性变量以降低所考虑模型的维数。之后，根据方程的参数对所有可能的相轨迹进行分类。还显示了一些行波和扭结波解决方案，并显示了图形表示来描述它们的传播。