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Boussinesq方程组的广义变分原理

曹小群 宋君强 张卫民 朱小谦 赵军

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Boussinesq方程组的广义变分原理

曹小群, 宋君强, 张卫民, 朱小谦, 赵军

Generalized variational principles for Boussinesq equation systems

Cao Xiao-Qun, Song Jun-Qiang, Zhang Wei-Min, Zhu Xiao-Qian, Zhao Jun
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  • 半反推法是何吉欢为了寻求物理问题的变分原理而提出的,可避免由拉氏乘子法引起的临界变分现象. 应用半反推法分别获得了描述水波运动的两类Boussinesq方程组的一族广义变分原理,并验证了它们的正确性.
    The semi-inverse method is proposed by He to establish the generalized variational principles for physical problems, which can eliminate variational crisis brought by the Lagrange multiplier method. Via the He s semi-inverse method, a family of variational principles is constructed for the Boussinesq equation systems and variant Boussinesq equation systems of fluid dynamics. The obtained variational principles have also proved to be correct.
    • 基金项目: 国家自然科学基金(批准号: 61070041,40775064)资助的课题.
    [1]

    Cai Q F, Huang S X, Gao S T, Zhong K, Li Z Q 2008 Acta Phys. Sin. 57 3912 (in Chinese) [蔡其发、 黄思训、 高守亭、 钟 科、 李自强 2008 物理学报 57 3912 ]

    [2]

    Wang Y G, Cai Q F, Huang S X 2010 Acta Phys. Sin. 59 4359 (in Chinese) [王业桂、 蔡其发、 黄思训 2010 物理学报 59 4359]

    [3]
    [4]

    Huang S X, Cai Q F, Xiang J, Zhang M 2007 Acta Phys. Sin. 56 3022 (in Chinese) [黄思训、 蔡其发、 项 杰、 张 铭 2007 物理学报 56 3022]

    [5]
    [6]
    [7]

    Cao X Q, Huang S X, Du H D 2008 Acta Phys. Sin. 57 3912 (in Chinese) [曹小群、 黄思训、 杜华栋 2008 物理学报 57 3912]

    [8]
    [9]

    Zhang L, Huang S X, Liu Y D, Zhong J 2010 Acta Phys. Sin. 59 2889 (in Chinese) [张 亮、 黄思训、 刘宇迪、 钟 剑 2010 物理学报 59 2889]

    [10]

    Huang S X, Zhao X F, Sheng Z 2009 Chin. Phys. B 18 5084

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    Zhang H B, Chen L Q, Liu R W 2005 Chin. Phys. B 14 1063

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    [14]

    Liu R W, Zhang H B, Chen L Q 2006 Chin. Phys. B 15 249

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    Li G C, Mei F X 2006 Chin. Phys. B 15 2496

    [18]

    Fu J L, Dai G D, Jimenez S, Tang Y F 2007 Chin. Phys. B 16 570

    [19]
    [20]
    [21]

    Shi S Y, Fu J L, Chen L Q 2008 Chin. Phys. B 17 385

    [22]
    [23]

    He J H 2008 Int. J. Mod. Phys. B 22 3487

    [24]
    [25]

    He J H 1997 Int. J. Turbo. Jet-Eng. 14 23

    [26]
    [27]

    He J H 2000 Appl. Math. Mech. 21 797

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    [29]

    He J H 2001 Int. J. Nonlin. Sci. Numer. 2 309

    [30]
    [31]

    He J H 2005 Phys. Lett. A 335 182

    [32]

    He J H 2007 Phys. Lett. A 371 39

    [33]
    [34]

    He J H, Lee E W M 2009 Phys. Lett. A 373 1644

    [35]
    [36]
    [37]

    Zheng C B, Liu B, Wang Z J, Zheng S K 2009 Int. J. Nonlin. Sci. Numer. 10 1369

    [38]
    [39]

    Zheng C B, Liu B, Wang Z J, Zheng S K 2009 Int. J. Nonlin. Sci. Numer. 10 1523

  • [1]

    Cai Q F, Huang S X, Gao S T, Zhong K, Li Z Q 2008 Acta Phys. Sin. 57 3912 (in Chinese) [蔡其发、 黄思训、 高守亭、 钟 科、 李自强 2008 物理学报 57 3912 ]

    [2]

    Wang Y G, Cai Q F, Huang S X 2010 Acta Phys. Sin. 59 4359 (in Chinese) [王业桂、 蔡其发、 黄思训 2010 物理学报 59 4359]

    [3]
    [4]

    Huang S X, Cai Q F, Xiang J, Zhang M 2007 Acta Phys. Sin. 56 3022 (in Chinese) [黄思训、 蔡其发、 项 杰、 张 铭 2007 物理学报 56 3022]

    [5]
    [6]
    [7]

    Cao X Q, Huang S X, Du H D 2008 Acta Phys. Sin. 57 3912 (in Chinese) [曹小群、 黄思训、 杜华栋 2008 物理学报 57 3912]

    [8]
    [9]

    Zhang L, Huang S X, Liu Y D, Zhong J 2010 Acta Phys. Sin. 59 2889 (in Chinese) [张 亮、 黄思训、 刘宇迪、 钟 剑 2010 物理学报 59 2889]

    [10]

    Huang S X, Zhao X F, Sheng Z 2009 Chin. Phys. B 18 5084

    [11]
    [12]

    Zhang H B, Chen L Q, Liu R W 2005 Chin. Phys. B 14 1063

    [13]
    [14]

    Liu R W, Zhang H B, Chen L Q 2006 Chin. Phys. B 15 249

    [15]
    [16]
    [17]

    Li G C, Mei F X 2006 Chin. Phys. B 15 2496

    [18]

    Fu J L, Dai G D, Jimenez S, Tang Y F 2007 Chin. Phys. B 16 570

    [19]
    [20]
    [21]

    Shi S Y, Fu J L, Chen L Q 2008 Chin. Phys. B 17 385

    [22]
    [23]

    He J H 2008 Int. J. Mod. Phys. B 22 3487

    [24]
    [25]

    He J H 1997 Int. J. Turbo. Jet-Eng. 14 23

    [26]
    [27]

    He J H 2000 Appl. Math. Mech. 21 797

    [28]
    [29]

    He J H 2001 Int. J. Nonlin. Sci. Numer. 2 309

    [30]
    [31]

    He J H 2005 Phys. Lett. A 335 182

    [32]

    He J H 2007 Phys. Lett. A 371 39

    [33]
    [34]

    He J H, Lee E W M 2009 Phys. Lett. A 373 1644

    [35]
    [36]
    [37]

    Zheng C B, Liu B, Wang Z J, Zheng S K 2009 Int. J. Nonlin. Sci. Numer. 10 1369

    [38]
    [39]

    Zheng C B, Liu B, Wang Z J, Zheng S K 2009 Int. J. Nonlin. Sci. Numer. 10 1523

计量
  • 文章访问数:  6590
  • PDF下载量:  768
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-10-18
  • 修回日期:  2010-11-19
  • 刊出日期:  2011-04-05

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