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Abstract
Using the Miura and Cole-Hopf transformations, we prove that ten sets of time independent symmetries of the Kaup-Kupershmidt equation constitute a non-Abelian Lie algebra. Ten hierarchies of equations corresponding to these ten sets of symme-tries possess a common strong symmetry. The time independent symmetries of ten hierarchies of integrable models and the Lie algebras constituted by these symmetries are also given.
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HAN PING²,

LOU SEN-YUE¹
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Cited By

[1]	Xin Xiang-Peng, Liu Han-Ze, Liu Xi-Qiang.Nonlocal symmetries and interaction solutions of the (2+1)-dimensional higher order Broer-Kaup system. Acta Physica Sinica, 2016, 65(24): 240202.doi:10.7498/aps.65.240202
[2]	Liu Yong, Liu Xi-Qiang.Exact solutions of Whitham-Broer-Kaup equations with variable coefficients. Acta Physica Sinica, 2014, 63(20): 200203.doi:10.7498/aps.63.200203
[3]	Wang Zhen-Li, Liu Xi-Qiang.Nonlocal symmetry and explicit solutions of the Kaup-Kupershmidt equation. Acta Physica Sinica, 2014, 63(18): 180205.doi:10.7498/aps.63.180205
[4]	Li Ning, Liu Xi-Qiang.Symmetries, reductions and exact solutions of Broer-Kau-Kupershmidt system. Acta Physica Sinica, 2013, 62(16): 160203.doi:10.7498/aps.62.160203
[5]	Lu Wei-Tao, Wang Shun-Jin, Zhang Hua.Algebraic dynamical algorithm for numerical solution of artificial earth satellite motion equation. Acta Physica Sinica, 2007, 56(7): 3655-3661.doi:10.7498/aps.56.3655
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[8]	Zhi Hong-Yan, Wang Qi, Zhang Hong-Qing.A series of new exact solutions to the (2+1)-dimensional Broer-Kau-Kupershmidt equation. Acta Physica Sinica, 2005, 54(3): 1002-1008.doi:10.7498/aps.54.1002
[9]	Zhu Jia-Min, Ma Zheng-Yi, Zheng Chun-Long.Localized fractal structure of the (2+1)-dimensional Broer-Kaup equations. Acta Physica Sinica, 2004, 53(10): 3248-3251.doi:10.7498/aps.53.3248
[10]	Naranmandula, Wang Ke-Xie.Multisoliton-like solutions for (2+1)-dimensional dispersive long wave equations and (2+1)-dimensional Broer-Kaup equations. Acta Physica Sinica, 2003, 52(7): 1565-1568.doi:10.7498/aps.52.1565
[11]	Zhao Xi-Qiang, Tang Deng-Bin, Wang Li-Min, Zhang Yiao-Ming.Some new soliton wave solutions for (2+1)-dimensional Broer-Kaup equations. Acta Physica Sinica, 2003, 52(8): 1827-1831.doi:10.7498/aps.52.1827
[12]	Zhang Jie-Fang, Han Peng.. Acta Physica Sinica, 2002, 51(4): 705-711.doi:10.7498/aps.51.705
[13]	Lin Ji, Wang Ke-Lin.. Acta Physica Sinica, 2001, 50(1): 13-20.doi:10.7498/aps.50.13
[14]	HAN PING, LOU SEN-YUE.NEW EXACT SOLUTIONS OF THE KAUP-KUPERSHMIDT EQUATION RELATED TO A NON-LOCAL SYMMETRY. Acta Physica Sinica, 1997, 46(7): 1249-1253.doi:10.7498/aps.46.1249
[15]	LIN JI, YU JUN, LOU SEN-YUE.(3+1)-DIMENSIONAL MODELS WITH INFINITELY DIMENSIONAL VIRASORO TYPE SYMMETRY ALGBRA. Acta Physica Sinica, 1996, 45(7): 1073-1080.doi:10.7498/aps.45.1073
[16]	Yu Jun.. Acta Physica Sinica, 1995, 44(5): 673-677.doi:10.7498/aps.44.673
[17]	QIANG WEN-CHAO.ALGEBRAIC PROPERTIES OF THE SEMI-PLANE-SYMMETRIC STATIC SPACE-TIME YIELDED BY SEMI-PLANE-SYMMETRIC NON-NULL ELECTROMAGNETIC FIELDS. Acta Physica Sinica, 1993, 42(4): 528-535.doi:10.7498/aps.42.528
[18]	RUAN HANG-YU, LOU SEN-YUE.SYMMETRY REDUCTIONS OF WHITHAM-BROER-KAUP EQUATIONS IN SHALLOW WATER. Acta Physica Sinica, 1992, 41(8): 1213-1221.doi:10.7498/aps.41.1213
[19]	WEI HUA.STRUCTURE CONSTANTS OF QUANTUM ALGEBRA AND YANG-BAXTER RELATION FOR THE Zn-SYMMETRIC STATISTICAL MODEL. Acta Physica Sinica, 1990, 39(9): 1357-1362.doi:10.7498/aps.39.1357
[20]	.. Acta Physica Sinica, 1975, 24(3): 215-222.doi:10.7498/aps.24.215

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Vol. 43, Issue 7 - 1994-04-05

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