In this work, we study a Buckley–Leverett equation of two-phase flow in porous media from the point of view of the Lie theory. We find that for some functions the equation has abundant exact solutions expressible in terms of Jacobi elliptic functions and consequently has many solutions in the form of periodic waves or solitary waves. We determine low-order conservation laws by using the multiplier method. From conservations laws, we construct the potential systems. From these systems we deduce potential equations. We study these equations from the point of view of Lie theory. Moreover, for these equations some nontrivial conservation laws are constructed by using the multipliers method.

中文翻译：

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Buckley-Leverett 方程的势系统：李点对称性和守恒定律

在这项工作中，我们从李理论的角度研究了多孔介质中两相流的巴克利-莱维特方程。我们发现对于某些函数，方程有丰富的精确解，可以用雅可比椭圆函数表示，因此有许多周期波或孤立波形式的解。我们使用乘法器方法确定低阶守恒定律。根据守恒定律，我们构建了潜在系统。从这些系统我们推导出潜在的方程。我们从李理论的角度研究这些方程。此外，对于这些方程，一些非平凡的守恒定律是通过使用乘法器方法构建的。