Conservation laws of the Hunter–Saxton equation for liquid crystal are constructed by using multipliers. Based on the obtained conservation laws, we construct a tree of partial differential equations systems nonlocally related to the Hunter–Saxton equation. Many new local and nonlocal symmetries for these systems are found. The equivalence transformations of two potential systems are obtained. A symmetry-based method is employed to construct nonlocally related inverse potential systems. The symmetry-based method does not rely on the existence of conservation laws for the original equation.

中文翻译：

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液晶Hunter-Saxton方程的守恒律和非局部相关系统

液晶的亨特-萨克斯顿方程的守恒律是通过使用乘法器构造的。基于获得的守恒律，我们构造了与Hunter–Saxton方程非局部相关的偏微分方程系统树。对于这些系统，发现了许多新的局部和非局部对称性。获得了两个潜在系统的等价变换。基于对称的方法可用于构造非局部相关的逆势系统。基于对称性的方法不依赖于原始方程的守恒定律。