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CDG方程和耦合KdV-MKdV方程的微分不变量

丁琦 郝爱晶

引用本文:
Citation:

CDG方程和耦合KdV-MKdV方程的微分不变量

丁琦, 郝爱晶

Differential invariants for CDG equation and coupled KDV-MKDV equations

Ding Qi, Hao Ai-Jing
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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.
    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.
    • 基金项目: 中央高校基本科研业务费(批准号:DUT13LK09)、辽宁省教育厅科学研究基金(批准号:L2012009)和国家自然科学基金(批准号:91230103)资助的课题.
    • Funds: Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. DUT13LK09), the Scientific Research Fund of Liaoning Provincial Education Department, China (Grant No. L2012009), and the National Natural Science Foundation of China (Grant No. 91230103).
    [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

  • [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

计量
  • 文章访问数:  1826
  • PDF下载量:  481
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-11-21
  • 修回日期:  2014-02-25
  • 刊出日期:  2014-06-05

CDG方程和耦合KdV-MKdV方程的微分不变量

  • 1. 大连理工大学数学科学学院, 大连 116024
    基金项目: 

    中央高校基本科研业务费(批准号:DUT13LK09)、辽宁省教育厅科学研究基金(批准号:L2012009)和国家自然科学基金(批准号:91230103)资助的课题.

摘要: 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.

English Abstract

参考文献 (22)

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