The symmetries of wave equations on new lattices

doi:10.1088/1674-1056/19/6/060301

中国物理B ›› 2010, Vol. 19 ›› Issue (6): 60301-060301.doi: 10.1088/1674-1056/19/6/060301

The symmetries of wave equations on new lattices

李晓伟¹, 何玉芳², 傅景礼²

(1)Department of Physics, Shangqiu Teacher College, Shangqiu 476000, China; (2)Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

收稿日期:2009-08-30 出版日期:2010-06-15 发布日期:2010-06-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No.~10672143).

The symmetries of wave equations on new lattices

He Yu-Fang(何玉芳)^a), Fu Jing-Li(傅景礼)^a)^†, and Li Xiao-Wei(李晓伟)^b)

^a Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; ^b Department of Physics, Shangqiu Teacher College, Shangqiu 476000, China

Received:2009-08-30 Online:2010-06-15 Published:2010-06-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No.~10672143).

摘要/Abstract

摘要： This paper focuses on studying the symmetry of a practical wave equation on new lattices. It is a new step in that the new lattice equation is applied to reduce the discrete problem of motion of an elastic thin homogeneous bar. The equation of motion of the bar can be changed into a discrete wave equation. With the new lattice equation, the translational and scaling invariant, not only is the infinitesimal transformation given, but the symmetry and Lie algebras are also calculated. We also give a new form of invariant called the ratio invariant, which can reduce the process of the computing invariant with the characteristic equation.

Abstract: This paper focuses on studying the symmetry of a practical wave equation on new lattices. It is a new step in that the new lattice equation is applied to reduce the discrete problem of motion of an elastic thin homogeneous bar. The equation of motion of the bar can be changed into a discrete wave equation. With the new lattice equation, the translational and scaling invariant, not only is the infinitesimal transformation given, but the symmetry and Lie algebras are also calculated. We also give a new form of invariant called the ratio invariant, which can reduce the process of the computing invariant with the characteristic equation.

Key words: new lattice equation, symmetry, discrete wave equation, invariant

中图分类号: (Lattice theory and statistics)

05.50.+q

02.10.Ud (Linear algebra)

何玉芳, 傅景礼, 李晓伟. The symmetries of wave equations on new lattices[J]. 中国物理B, 2010, 19(6): 60301-060301.

He Yu-Fang(何玉芳), Fu Jing-Li(傅景礼), and Li Xiao-Wei(李晓伟). The symmetries of wave equations on new lattices[J]. Chin. Phys. B, 2010, 19(6): 60301-060301.

参考文献 25

[1]	Mei F X 1999 Applications of Lie Group and Lie Algebra to Constraint Mechanical Systems (Beijing: Science Press)
[2]	Liu C, Mei F X and Guo Y X 2009 Chin. Phys. B 18 395
[3]	Chen Y D, Li L, Zhang Y and Hu J M 2009 Chin. Phys. B 18 1373
[4]	Shang M and Mei F X 2009 Chin. Phys. B 18 3155
[5]	Fu J L, Chen B Y and Xie F P 2008 Chin. Phys. B 17 4354
[6]	Zhang H B, Chen L Q and Liu R W 2005 Chin. Phys. 14 238
[7]	Chen X W, Liu C M and Liu Y M 2006 Chin. Phys. 15 470
[8]	Lou Z M 2006 Chin. Phys. 15 891
[9]	Fang J H, Liao Y P, Ding N and Wang P 2006 Chin. Phys. 15 2792
[10]	Guo Y X, Jing L Y and Yu Y 2001 Chin. Phys. 10 181
[11]	Zhang Y, Shang M and Mei F X 2000 Chin. Phys. 9 401
[12]	Zhang Y 2009 Chin. Phys. B 18 4636
[13]	Li Y C, Xia L L and Wang X M 2009 Chin. Phys. B 18 4643
[14]	Zhang H B, Chen L Q and Liu R W 2005 Chin. Phys. 14 888
[15]	Liu R W, Zhang H B and Chen L Q 2006 Chin. Phys. 15 249
[16]	Fu J L, Chen L Q and Chen B Y 2009 Sci. Chin. 39 1320 (in Chinese)
[17]	Fu J L, Chen L Q and Chen B Y 2010 Sci. Chin. 40 133 (in Chinese)
[18]	Fu J L, Chen L Q and Chen B Y 2009 Phys. Lett. A 373 409
[19]	Hernandez P and Sundrum R 1996 Phys. Lett. 385 254
[20]	Gandarias M L, Torrisi and Valenti M A 2004 International Journal of Non-linear Mechanics 39 389
[21]	Levi D and Winternitz P 2002 J. Phys. A : Math. Gen. 35 2249
[22]	Zhang M J, Fang J H, Zhang X N and Lu K 2008 Chin. Phys. B 17 1957
[23]	Bluman G W and Kumei S 1991 Symmetries and Differential Equations (Beijing: World Publishing Corporation) p.~80
[24]	Xia L L, Cai J L and Li Y C 2009 Chin. Phys. B 18 3158
[25]	Li R J, Qiao Y F and Zhao S H 2006 Acta Phys. Sin. 55 5598 (in Chinese)

The symmetries of wave equations on new lattices

The symmetries of wave equations on new lattices

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 25

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Shu-Qi Xue(薛书琦), Nirajan Shiwakoti, Xiao-Meng Shi(施晓蒙), and Yao Xiao(肖尧). Investigating the characteristic delay time in the leader-follower behavior in children single-file movement[J]. 中国物理B, 2023, 32(2): 28901-028901.
[2]	Guan-Ning Wang(王冠宁), Tao Chen(陈涛), Jin-Wei Chen(陈锦炜), Kaifeng Deng(邓凯丰), and Ru-Dong Wang(王汝栋). Simulation of crowd dynamics in pedestrian evacuation concerning panic contagion: A cellular automaton approach[J]. 中国物理B, 2022, 31(6): 60402-060402.
[3]	Hui Jiang and Ching Hua Lee. Filling up complex spectral regions through non-Hermitian disordered chains[J]. 中国物理B, 2022, 31(5): 50307-050307.
[4]	Hui-Qiang Liang(梁辉强) and Linhu Li(李林虎). Topological properties of non-Hermitian Creutz ladders[J]. 中国物理B, 2022, 31(1): 10310-010310.
[5]	Jiayue Wang(王嘉悦), Maik Boltes, Armin Seyfried, Antoine Tordeux, Jun Zhang(张俊), and Wenguo Weng(翁文国). Experimental study on age and gender differences in microscopic movement characteristics of students[J]. 中国物理B, 2021, 30(9): 98902-098902.
[6]	. [J]. 中国物理B, 2021, 30(3): 30504-.
[7]	. [J]. 中国物理B, 2021, 30(2): 20504-0.
[8]	谭志中, 谭震. Electrical properties of m×n cylindrical network[J]. 中国物理B, 2020, 29(8): 80503-080503.
[9]	刘宏芳, 苏子贤, 张智强, 江华. Topological Anderson insulator in two-dimensional non-Hermitian systems[J]. 中国物理B, 2020, 29(5): 50502-050502.
[10]	覃章荣, 陈燕雁, 凌风如, 孟令娟, 张超英. A mass-conserved multiphase lattice Boltzmann method based on high-order difference[J]. 中国物理B, 2020, 29(3): 34701-034701.
[11]	马亚萍, 张辉. Simulation study on cooperation behaviors and crowd dynamics in pedestrian evacuation[J]. 中国物理B, 2020, 29(3): 38901-038901.
[12]	陈长坤, 童蕴贺. Evacuation simulation considering action of guard in artificial attack[J]. 中国物理B, 2019, 28(1): 10503-010503.
[13]	文军, 张建奇, 闫磊磊, 冯芒. Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams[J]. 中国物理B, 2019, 28(1): 10306-010306.
[14]	张涛, 任刚, 俞志钢, 杨阳. Model and application of bidirectional pedestrian flows at signalized crosswalks[J]. 中国物理B, 2018, 27(7): 78901-078901.
[15]	谭志中. Recursion-transform method and potential formulae of the m×n cobweb and fan networks[J]. 中国物理B, 2017, 26(9): 90503-090503.