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本文利用了Olver提出的等价活动标架方法，通过构造合适的活动标架，得到了CDG方程和耦合KdV-MKdV方程的微分不变量，并推得了微分不变量代数.
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关键词:
- 微分不变量 /
- 活动标架 /
- CDG方程 /
- 耦合KdV-MKdV方程
In this paper, the differential invariants of Lie symmetry groups of the CDG equation and the coupled KdV-MKdV equations are obtained. Their syzygies and recurrence relations are classified, which are based on the algorithms of equivariant moving frames.-
Keywords:
- differential invariants /
- equivariant moving frames /
- CDG equation /
- coupled KdV-MKdV equations
[1] Lou Z M 2010 Acta Phys. Sin. 59 6764 (in Chinese)[楼智美 2010 物理学报 59 6764]
[2] Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4659 (in Chinese) [梅凤翔, 蔡建乐 2008 物理学报 57 4659]
[3] Li Hongguo, Huang Kefu 2013 Chin. Phy. Lett. 30 027101
[4] Fang Jianhui, Ding Ning, Chen Xiangxia 2008 Chin. Phys. B 17 1967
[5] Ding Ning, Fang Jianhui 2009 Acta Phys. Sin. 58 7440 (in Chinese) [丁宁, 方建会 2009 物理学报 58 7440]
[6] Fels M, Olver P J 1999 Acta Appl. Math. 55 127
[7] Cheh J, Olver P J, Pohjanpelto J 2005 J. Math. Phys. 46 023504
[8] Olver P J, Pohjapelto J 2007 Arkiv. Mat. 50 165
[9] Olver P J, Pohjapelto J 2008 Canadian J. Math. 60 1336
[10] Olver P J 2011 Comtemp. Math. 549 95
[11] Hubert E, Kogan I A 2007 Found. Comput. Math. 455
[12] Hubert E 2009 Journal of Symbolic Computation 44 382
[13] Li W, Li W T, Wang F, Zhang H Q 2013 Commun. Nonlinear Sci. Number. Sinulat 18 888
[14] Gou M Y, Gao J 2009 Acta Phys. Sin. 58 6686 (in Chinese) [郭美玉, 高洁 2009 物理学报 58 6686]
[15] Sawada K, T Kotera 1974 Prog. Theor. Phys. 51 1355
[16] Caudrey P J, Dodd R K, J D Gibbon 1976 Proc. R. Soc. Lond. A 1976 351
[17] Dogan Kaya, El-Sayed S M 2003 Phys. Lett. 328 274
[18] Yang L, Zhang F, Wang Y H 2002 Chaos, Solitons and Fractals 13 337
[19] Biswas A, Ebadi G, Triki H, Yildirim A, Yousefzadeh N 2013 Results in Math. C 3 687
[20] Xia T C, Yue C 2013 5th CM 2013 Changchun, China, Augest 18
[21] Olver P J 1995 Applications of Lie Groups to Differential Equations (Cambridge University Press)
[22] Chen J, POlver J, Phojanpelto J 2008 Found. Comput. Math. 8 501
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[1] Lou Z M 2010 Acta Phys. Sin. 59 6764 (in Chinese)[楼智美 2010 物理学报 59 6764]
[2] Mei F X, Cai J L 2008 Acta Phys. Sin. 57 4659 (in Chinese) [梅凤翔, 蔡建乐 2008 物理学报 57 4659]
[3] Li Hongguo, Huang Kefu 2013 Chin. Phy. Lett. 30 027101
[4] Fang Jianhui, Ding Ning, Chen Xiangxia 2008 Chin. Phys. B 17 1967
[5] Ding Ning, Fang Jianhui 2009 Acta Phys. Sin. 58 7440 (in Chinese) [丁宁, 方建会 2009 物理学报 58 7440]
[6] Fels M, Olver P J 1999 Acta Appl. Math. 55 127
[7] Cheh J, Olver P J, Pohjanpelto J 2005 J. Math. Phys. 46 023504
[8] Olver P J, Pohjapelto J 2007 Arkiv. Mat. 50 165
[9] Olver P J, Pohjapelto J 2008 Canadian J. Math. 60 1336
[10] Olver P J 2011 Comtemp. Math. 549 95
[11] Hubert E, Kogan I A 2007 Found. Comput. Math. 455
[12] Hubert E 2009 Journal of Symbolic Computation 44 382
[13] Li W, Li W T, Wang F, Zhang H Q 2013 Commun. Nonlinear Sci. Number. Sinulat 18 888
[14] Gou M Y, Gao J 2009 Acta Phys. Sin. 58 6686 (in Chinese) [郭美玉, 高洁 2009 物理学报 58 6686]
[15] Sawada K, T Kotera 1974 Prog. Theor. Phys. 51 1355
[16] Caudrey P J, Dodd R K, J D Gibbon 1976 Proc. R. Soc. Lond. A 1976 351
[17] Dogan Kaya, El-Sayed S M 2003 Phys. Lett. 328 274
[18] Yang L, Zhang F, Wang Y H 2002 Chaos, Solitons and Fractals 13 337
[19] Biswas A, Ebadi G, Triki H, Yildirim A, Yousefzadeh N 2013 Results in Math. C 3 687
[20] Xia T C, Yue C 2013 5th CM 2013 Changchun, China, Augest 18
[21] Olver P J 1995 Applications of Lie Groups to Differential Equations (Cambridge University Press)
[22] Chen J, POlver J, Phojanpelto J 2008 Found. Comput. Math. 8 501
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