Conservation laws and nonlocally related systems of the Hunter-Saxton equation for liquid crystal

被引：38
作者：
Zhao, Zhonglong [1 ]
机构：
[1] North Univ China, Dept Math, Taiyuan 030051, Shanxi, Peoples R China
来源：
ANALYSIS AND MATHEMATICAL PHYSICS | 2019年 / 9卷 / 04期
关键词：
Hunter-Saxton equation; Nonlocally related systems; Inverse potential systems; Conservation laws; 76M60; 70S10; 54H15; PARTIAL-DIFFERENTIAL-EQUATIONS; ALGEBRO-GEOMETRIC SOLUTIONS; DIRECT CONSTRUCTION METHOD; EQUIVALENCE TRANSFORMATIONS; POTENTIAL SYSTEMS; NOETHERS THEOREM; LUMP SOLUTIONS; SYMMETRIES; COMPUTATION;
D O I：
10.1007/s13324-019-00337-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：2311 / 2327
页数：17
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