Conservation laws and nonlocally related systems of the Hunter–Saxton equation for liquid crystal
作者： Zhonglong Zhao
DOI: 10.1007/S13324-019-00337-3
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摘要: Conservation laws of the Hunter–Saxton equation for liquid crystal are constructed by using multipliers. Based on obtained conservation laws, we construct a tree partial differential equations systems nonlocally related to equation. Many new local and nonlocal symmetries these found. The equivalence transformations two potential obtained. A symmetry-based method is employed inverse systems. does not rely existence original
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sci-hub.se 参考文章(49)
Stephen C. Anco, George W. Bluman, Alexei F. Cheviakov, Applications of Symmetry Methods to Partial Differential Equations ,(2011)
Zhengzheng Yang, George W. Bluman, A Symmetry-Based Method for Constructing Nonlocally Related PDE Systems arXiv: Mathematical Physics. ,(2012) , 10.1063/1.4819724
Stephen C. Anco, George W. Bluman, Symmetry and Integration Methods for Differential Equations ,(2002)
Nail H. Ibragimov, Nonlinear self-adjointness in constructing conservation laws arXiv: Mathematical Physics. ,(2011)
George Bluman, Alexei F. Cheviakov, Nataliya M. Ivanova, Framework for nonlocally related partial differential equation systems and nonlocal symmetries: Extension, simplification, and examples Journal of Mathematical Physics. ,vol. 47, pp. 113505- ,(2006) , 10.1063/1.2349488
R. Naz, F.M. Mahomed, D.P. Mason, Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics Applied Mathematics and Computation. ,vol. 205, pp. 212- 230 ,(2008) , 10.1016/J.AMC.2008.06.042
Zhengzheng Yang, Alexei F. Cheviakov, Some relations between symmetries of nonlocally related systems Journal of Mathematical Physics. ,vol. 55, pp. 083514- ,(2014) , 10.1063/1.4891491
A. S. Fokas, A unified transform method for solving linear and certain nonlinear PDEs Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. ,vol. 453, pp. 1411- 1443 ,(1997) , 10.1098/RSPA.1997.0077
Alberto Bressan, Adrian Constantin, Global Solutions of the Hunter--Saxton Equation Siam Journal on Mathematical Analysis. ,vol. 37, pp. 996- 1026 ,(2005) , 10.1137/050623036
Stephen C. Anco, George Bluman, Direct Construction of Conservation Laws from Field Equations Physical Review Letters. ,vol. 78, pp. 2869- 2873 ,(1997) , 10.1103/PHYSREVLETT.78.2869