Please wait a minute...
Chin. Phys. B, 2011, Vol. 20(2): 021101    DOI: 10.1088/1674-1056/20/2/021101

Lie symmetry and Mei conservation law of continuum system

Shi Shen-Yang, Fu Jing-Li
Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
Abstract  Lie symmetry and Mei conservation law of continuum Lagrange system are studied in this paper. The equation of motion of continuum system is established by using variational principle of continuous coordinates. The invariance of the equation of motion under an infinitesimal transformation group is determined to be Lie-symmetric. The condition of obtaining Mei conservation theorem from Lie symmetry is also presented. An example is discussed for applications of the results.
Keywords:  Mei symmetry      conservation law      continuum mechanics      Lie symmetry  
Received:  17 July 2010      Revised:  02 September 2010      Published:  15 February 2011
PACS:  11.30.-j (Symmetry and conservation laws)  
  83.10.Ff (Continuum mechanics)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11072218) and the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6100337).

Cite this article: 

Shi Shen-Yang, Fu Jing-Li Lie symmetry and Mei conservation law of continuum system 2011 Chin. Phys. B 20 021101

[1] Marsden J E and Ratiu T S 1994 Introduction to Mechanics and Symmetry (New York: Springer-Verlag)
[2] Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese)
[3] Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)
[4] Lou S K and Zhang Y F 2008 Advances in the Study of Dynamics of Constrained Systems (Beijing: Science Press) (in Chinese)
[5] Armstrong M A 1997 Group and Symmetry (New York: Springer-Verlag)
[6] Olver P J 1999 Applications of Lie Groups to Differential Equations (New York: Springer-Verlag)
[7] Bluman G W and Anco S C 2004 Symmetry and Integration Methods for Differential Equations (New York: Springer-Verlag)
[8] Haas F and Goedert J 2000 J. Phys. A: Math. Gen. 33 4661
[9] Chavarriga J, Garc'hia I A and Gin'e J 2001 Nonlinearity 14 863
[10] Aleynikov D V and Tolkachev E A 2003 J. Phys. A: Math. Gen. 36 2251
[11] Baker T W and Tavel M A 1974 Am. T. Phys. 42 857
[12] Rosen J 1972 Ann. Phys. 69 349
[13] Djuki'c Dj 1974 Archives of Mech. 26 243
[14] Sarlet W and Cantrijn F 1981 SIAM Rev. 23 467
[15] Bahar L Y and Kanty H G 1987 Int. J. Nonlinear Mech. 22 125
[16] Ge W K 2007 Acta Phys. Sin. 56 1 (in Chinese)
[17] Liu H J, Fu J L and Tang Y F 2007 Chin. Phys. 16 599
[18] Fang J H, Ding N and Wang P 2007 Acta Phys. Sin. 56 3039 (in Chinese)
[19] Zheng S W and Jia L Q 2007 Acta Phys. Sin. 56 661 (in Chinese)
[20] Fang J H, Ding N and Wang P 2007 Chin. Phys. 16 887
[1] Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws
Xian-Guo Geng(耿献国), Fei-Ying Guo(郭飞英), Yun-Yun Zhai(翟云云). Chin. Phys. B, 2020, 29(5): 050201.
[2] An extension of integrable equations related to AKNS and WKI spectral problems and their reductions
Xian-Guo Geng(耿献国), Yun-Yun Zhai(翟云云). Chin. Phys. B, 2018, 27(4): 040201.
[3] A local energy-preserving scheme for Zakharov system
Qi Hong(洪旗), Jia-ling Wang(汪佳玲), Yu-Shun Wang(王雨顺). Chin. Phys. B, 2018, 27(2): 020202.
[4] Residual symmetry, interaction solutions, and conservation laws of the (2+1)-dimensional dispersive long-wave system
Ya-rong Xia(夏亚荣), Xiang-peng Xin(辛祥鹏), Shun-Li Zhang(张顺利). Chin. Phys. B, 2017, 26(3): 030202.
[5] Local structure-preserving methods for the generalized Rosenau-RLW-KdV equation with power law nonlinearity
Jia-Xiang Cai(蔡加祥), Qi Hong(洪旗), Bin Yang(杨斌). Chin. Phys. B, 2017, 26(10): 100202.
[6] Conformal structure-preserving method for damped nonlinear Schrödinger equation
Hao Fu(傅浩), Wei-En Zhou(周炜恩), Xu Qian(钱旭), Song-He Song(宋松和), Li-Ying Zhang(张利英). Chin. Phys. B, 2016, 25(11): 110201.
[7] A new six-component super soliton hierarchy and its self-consistent sources and conservation laws
Han-yu Wei(魏含玉) and Tie-cheng Xia(夏铁成). Chin. Phys. B, 2016, 25(1): 010201.
[8] Multi-symplectic variational integrators for nonlinear Schrödinger equations with variable coefficients
Cui-Cui Liao(廖翠萃), Jin-Chao Cui(崔金超), Jiu-Zhen Liang(梁久祯), Xiao-Hua Ding(丁效华). Chin. Phys. B, 2016, 25(1): 010205.
[9] A local energy-preserving scheme for Klein–Gordon–Schrödinger equations
Cai Jia-Xiang, Wang Jia-Lin, Wang Yu-Shun. Chin. Phys. B, 2015, 24(5): 050205.
[10] Conservation laws of the generalized short pulse equation
Zhang Zhi-Yong, Chen Yu-Fu. Chin. Phys. B, 2015, 24(2): 020201.
[11] Conservative method for simulation of a high-order nonlinear Schrödinger equation with a trapped term
Cai Jia-Xiang, Bai Chuan-Zhi, Qin Zhi-Lin. Chin. Phys. B, 2015, 24(10): 100203.
[12] A novel hierarchy of differential–integral equations and their generalized bi-Hamiltonian structures
Zhai Yun-Yun, Geng Xian-Guo, He Guo-Liang. Chin. Phys. B, 2014, 23(6): 060201.
[13] Riccati-type Bäcklund transformations of nonisospectral and generalized variable-coefficient KdV equations
Yang Yun-Qing, Wang Yun-Hu, Li Xin, Cheng Xue-Ping. Chin. Phys. B, 2014, 23(3): 030506.
[14] A conservative Fourier pseudospectral algorithm for the nonlinear Schrödinger equation
Lv Zhong-Quan, Zhang Lu-Ming, Wang Yu-Shun. Chin. Phys. B, 2014, 23(12): 120203.
[15] Lie symmetry theorem of fractional nonholonomic systems
Sun Yi, Chen Ben-Yong, Fu Jing-Li. Chin. Phys. B, 2014, 23(11): 110201.
No Suggested Reading articles found!