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

被引：1
作者：
Zhonglong Zhao
机构：
[1] North University of China,Department of Mathematics
来源：
Analysis and Mathematical Physics | 2019年 / 9卷
关键词：
Hunter–Saxton equation; Nonlocally related systems; Inverse potential systems; Conservation laws; 76M60; 70S10; 54H15;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
页码：2311 / 2327
页数：16
相关论文
共 87 条
[1]  
Ma WX(2018)Diversity of interaction solutions to the Comput. Math. Appl. 75 289-295
[2]  
Yong XL(2018)-dimensional Ito equation J. Differ. Equ. 264 2633-2659
[3]  
Zhang HQ(2017)Lump solutions to nonlinear partial differential equations via Hirota bilinear forms Mod. Phys. Lett. B 31 1750157-121
[4]  
Ma WX(2019)Lump soliton, mixed lump stripe and periodic lump solutions of a Appl. Math. Lett. 95 114-2676
[5]  
Zhou Y(2012)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation Phys. Rev. E 86 016601-17
[6]  
Zhao ZL(2017)Multiple lump solutions of the Nonlinear Dyn. 87 2661-266
[7]  
Chen Y(2017)-dimensional potential Yu–Toda–Sasa–Fukuyama equation Optik Int. J. Light Electron Opt. 140 10-89
[8]  
Han B(2008)Negative-order Korteweg–de Vries equations J. Phys. A Math. Theor. 41 355209-1443
[9]  
Zhao ZL(2004)The Riemann–Bäcklund method to a quasiperiodic wave solvable generalized variable coefficient Phys. A Stat. Mech. Appl. 339 248-354
[10]  
He LC(2017)-dimensional KdV equation Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 473 20170232-234
123456789