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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.
[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
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[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
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