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Generalized variational principles for three kinds of atmospheric waves

Song Jun-Qiang Cao Xiao-Qun Zhu Xiao-Qian Zhang Wei-Min Zhao Jun

Generalized variational principles for three kinds of atmospheric waves

Song Jun-Qiang, Cao Xiao-Qun, Zhu Xiao-Qian, Zhang Wei-Min, Zhao Jun
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  • The semi-inverse method is proposed by He to establish generalized variational principles for mathematical and physical problems, in which the variational crisis brought by the Lagrange multiplier method can be eliminated. with He's semi-inverse method, a family of variational principles is constructed for Rossby wave, atmospheric acoustic wave and gravity wave respectively. The obtained variational principles have also proved correct.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 41105063, 61070041).
    [1]

    Zhang L, Huang S X, Liu Y D, Zhong J 2010 Acta Phys. Sin. 592889 (in chinese)[张亮, 黄思训, 刘宇迪, 钟剑 2010 物理学报 59 2889]

    [2]
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    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]

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

    [7]
    [8]

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

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

    [11]

    Fu J L, Dai G D 2007 Chin. Phys. 16 570

    [12]
    [13]
    [14]

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

    [15]

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

    [16]
    [17]
    [18]

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

    [19]

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

    [20]
    [21]
    [22]

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

    [23]

    He J H 2005 Phys. Lett. A 335 182

    [24]
    [25]

    He J H 2007 Phys. Lett. A 371 39

    [26]
    [27]

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

    [28]
    [29]

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

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    L M Z, Peng Y Q 1990 Dynamical Meteorology (Beijing: MeteorologyPress) p25 (in Chinese)[吕美仲, 彭永清 1990 动力气象(北京:气象出版社) 第25页]

    [33]
    [34]

    Huang S X, Wu R S 2001 Methods of Mathematical Physics inAtmospheric Science (Beijing: China Meteorologica Press) p154[黄思训, 伍荣生 2001 大气科学中的数学物理问题(北京:气象出版社) 第154页]

    [35]

    Li C Y, Liu S K, Chen J B 2005 Introduction of Dynamical Meteorology(Beijing: China Meteorologica Press) p45 [李崇银, 刘式适, 陈嘉滨 2005 动力气象学导论(北京:气象出版社)第45页]

  • [1]

    Zhang L, Huang S X, Liu Y D, Zhong J 2010 Acta Phys. Sin. 592889 (in chinese)[张亮, 黄思训, 刘宇迪, 钟剑 2010 物理学报 59 2889]

    [2]
    [3]
    [4]

    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]

    [5]
    [6]

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

    [7]
    [8]

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

    [9]
    [10]

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

    [11]

    Fu J L, Dai G D 2007 Chin. Phys. 16 570

    [12]
    [13]
    [14]

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

    [15]

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

    [16]
    [17]
    [18]

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

    [19]

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

    [20]
    [21]
    [22]

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

    [23]

    He J H 2005 Phys. Lett. A 335 182

    [24]
    [25]

    He J H 2007 Phys. Lett. A 371 39

    [26]
    [27]

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

    [28]
    [29]

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

    [30]
    [31]
    [32]

    L M Z, Peng Y Q 1990 Dynamical Meteorology (Beijing: MeteorologyPress) p25 (in Chinese)[吕美仲, 彭永清 1990 动力气象(北京:气象出版社) 第25页]

    [33]
    [34]

    Huang S X, Wu R S 2001 Methods of Mathematical Physics inAtmospheric Science (Beijing: China Meteorologica Press) p154[黄思训, 伍荣生 2001 大气科学中的数学物理问题(北京:气象出版社) 第154页]

    [35]

    Li C Y, Liu S K, Chen J B 2005 Introduction of Dynamical Meteorology(Beijing: China Meteorologica Press) p45 [李崇银, 刘式适, 陈嘉滨 2005 动力气象学导论(北京:气象出版社)第45页]

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  • Received Date:  13 July 2011
  • Accepted Date:  05 April 2012
  • Published Online:  05 April 2012

Generalized variational principles for three kinds of atmospheric waves

  • 1. School of Computer Science, National University of Defense Technology, Changsha 410073, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 41105063, 61070041).

Abstract: The semi-inverse method is proposed by He to establish generalized variational principles for mathematical and physical problems, in which the variational crisis brought by the Lagrange multiplier method can be eliminated. with He's semi-inverse method, a family of variational principles is constructed for Rossby wave, atmospheric acoustic wave and gravity wave respectively. The obtained variational principles have also proved correct.

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