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A solving problem for the Lorenz system in atmospheric physics is considered. First, a set of variational iterations is constructed by using the generalized variation principle. Then, the initial approximate solution is determined. Finally, using the variational iteration, each approximate solution for corresponding model is found. The generalized variational iteration method is an analytic method, and the obtained solution can be analytically operated further.
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Keywords:
- Lorenz equation /
- variation principle /
- approximate solution
[1] McPhaden M J, Zhang D 2002 Nature 415 603
[2] [3] Gu D F, Philander S G H 1997 Science 275 805
[4] [5] Yaremchuk M, Qu T 2004 J. Phys. Oceanogr. 34 844
[6] Woodworth P L 2006 Phil. Trans. R. Soc. A 364 787
[7] [8] Jacobs S 2006 Phil. Trans. R. Soc. A 364 1657
[9] [10] [11] Wang, D, Liu, Q, Huang R X, Du Y, Qu T 2006 Geophys. Res. Lett. 33 L14605
[12] [13] Palmer, M D, Hames, K, Tett S F, Ansell B 2007 Geophys. Ret. Lett. 34 L23610
[14] Lozier M S, Leadbetter S, Willians R G, Roussenov V, Reed M S C, Moore N J 2008 Science 319 800
[15] [16] [17] Emanuel K A 1979 J. Atm. Sci. 36 2425
[18] Sun W Y 1995 J. Meteorol. Soc. 121 419
[19] [20] [21] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[22] Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392.
[23] [24] [25] Ei Shin-Ichiro, Matsuzawa H 2010 Disc. Contin. Dyn. Syst. 26 910
[26] Kellogg R B, Kopteva N 2010 J. Differ. Eqns. 248 184
[27] [28] Zhou X C, Lin Y H, Lin W T, Mo J Q 2009 Acta Oceanologica Sin. 28 1
[29] [30] [31] Zhou X C, Lin Y H, Lin W T, Mo J Q 2009 Chin. Phys. B 18 4603
[32] [33] Zhou X C, Lin W T, Lin Y H, Mo J Q 2010 Acta Phys. Sin. 59 2173 (in Chinese)[周先春、林万涛、林一骅、莫嘉琪 2010 物理学报 59 2173]
[34] [35] Mo J Q, Wang H, Lin W T, Lin Y H 2006 Acta Phys.Sin. 55 6(in Chinese)[莫嘉琪、王 辉、林万涛、林一骅 2006 物理学报 55 6]
[36] [37] Mo J Q, Wang H, Lin W T 2006 Acta Phys.Sin. 55 3229(in Chinese)[莫嘉琪、王 辉、林万涛 2006 物理学报 55 3229]
[38] Mo J Q, Lin W T, Lin Y H 2007 Acta Phys.Sin. 56 3127(in Chinese)[莫嘉琪、林万涛、林一骅 2006 物理学报 56 3127]
[39] [40] [41] Mo J Q, Lin W T 2007 Acta Phys.Sin. 56 5565(in Chinese)[莫嘉琪, 林万涛 2007 物理学报 56 5565]
[42] [43] Mo J Q, Lin W T 2008 Acta Phys.Sin. 57 1291(in Chinese)[莫嘉琪、林万涛 2008 物理学报 57 1291]
[44] [45] Mo J Q, Lin W T, Lin Y H 2008 Chin. Phys. B 17 370
[46] [47] Mo J Q, Lin W T, Lin Y H 2008 Chin. Phys. B 17 743
[48] Mo J Q, Lin Y H, Lin W T 2009 Acta Phys. Sin. 58 6692 (in Chinese)[莫嘉琪、林一骅、林万涛 2009 物理学报 58 6692]
[49] [50] Mo J Q, Lin Y H, Lin W T 2010 Acta Phys. Sin. 59 6701 (in Chinese)[莫嘉琪、林一骅、林万涛 2010 物理学报 59 6701]
[51] [52] Mo J Q 2011 Acta Phys. Sin. 60 020202 (in Chinese) [莫嘉琪 2011 物理学报 60 020202]
[53] [54] [55] Mo J Q, Lin W T, Lin Y H 2009 Chin. Phys. B 18 3624
[56] [57] Xie F, Lin W T, Lin Y H, Mo J Q 2011 Chin. Phys. B 20 010208.
[58] He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese)[何吉欢 2002 工程和科学计算中的近似分析方法 (郑州: 河南科学技术出版社)]
[59] [60] [61] Chou J F 2002 Nonlinear and complexity in Atmospheric Sciences (Beijing: China Meteorological Press) (in Chineae)[丑纪范 2002 大气科学中的非线性与复杂性 (北京: 气象出版社)]
[62] Jordan D W, Smith P 1977 Nonlinear Ordinary Differential Equations (Oxford: Oxford University Press)
[63] -
[1] McPhaden M J, Zhang D 2002 Nature 415 603
[2] [3] Gu D F, Philander S G H 1997 Science 275 805
[4] [5] Yaremchuk M, Qu T 2004 J. Phys. Oceanogr. 34 844
[6] Woodworth P L 2006 Phil. Trans. R. Soc. A 364 787
[7] [8] Jacobs S 2006 Phil. Trans. R. Soc. A 364 1657
[9] [10] [11] Wang, D, Liu, Q, Huang R X, Du Y, Qu T 2006 Geophys. Res. Lett. 33 L14605
[12] [13] Palmer, M D, Hames, K, Tett S F, Ansell B 2007 Geophys. Ret. Lett. 34 L23610
[14] Lozier M S, Leadbetter S, Willians R G, Roussenov V, Reed M S C, Moore N J 2008 Science 319 800
[15] [16] [17] Emanuel K A 1979 J. Atm. Sci. 36 2425
[18] Sun W Y 1995 J. Meteorol. Soc. 121 419
[19] [20] [21] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[22] Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392.
[23] [24] [25] Ei Shin-Ichiro, Matsuzawa H 2010 Disc. Contin. Dyn. Syst. 26 910
[26] Kellogg R B, Kopteva N 2010 J. Differ. Eqns. 248 184
[27] [28] Zhou X C, Lin Y H, Lin W T, Mo J Q 2009 Acta Oceanologica Sin. 28 1
[29] [30] [31] Zhou X C, Lin Y H, Lin W T, Mo J Q 2009 Chin. Phys. B 18 4603
[32] [33] Zhou X C, Lin W T, Lin Y H, Mo J Q 2010 Acta Phys. Sin. 59 2173 (in Chinese)[周先春、林万涛、林一骅、莫嘉琪 2010 物理学报 59 2173]
[34] [35] Mo J Q, Wang H, Lin W T, Lin Y H 2006 Acta Phys.Sin. 55 6(in Chinese)[莫嘉琪、王 辉、林万涛、林一骅 2006 物理学报 55 6]
[36] [37] Mo J Q, Wang H, Lin W T 2006 Acta Phys.Sin. 55 3229(in Chinese)[莫嘉琪、王 辉、林万涛 2006 物理学报 55 3229]
[38] Mo J Q, Lin W T, Lin Y H 2007 Acta Phys.Sin. 56 3127(in Chinese)[莫嘉琪、林万涛、林一骅 2006 物理学报 56 3127]
[39] [40] [41] Mo J Q, Lin W T 2007 Acta Phys.Sin. 56 5565(in Chinese)[莫嘉琪, 林万涛 2007 物理学报 56 5565]
[42] [43] Mo J Q, Lin W T 2008 Acta Phys.Sin. 57 1291(in Chinese)[莫嘉琪、林万涛 2008 物理学报 57 1291]
[44] [45] Mo J Q, Lin W T, Lin Y H 2008 Chin. Phys. B 17 370
[46] [47] Mo J Q, Lin W T, Lin Y H 2008 Chin. Phys. B 17 743
[48] Mo J Q, Lin Y H, Lin W T 2009 Acta Phys. Sin. 58 6692 (in Chinese)[莫嘉琪、林一骅、林万涛 2009 物理学报 58 6692]
[49] [50] Mo J Q, Lin Y H, Lin W T 2010 Acta Phys. Sin. 59 6701 (in Chinese)[莫嘉琪、林一骅、林万涛 2010 物理学报 59 6701]
[51] [52] Mo J Q 2011 Acta Phys. Sin. 60 020202 (in Chinese) [莫嘉琪 2011 物理学报 60 020202]
[53] [54] [55] Mo J Q, Lin W T, Lin Y H 2009 Chin. Phys. B 18 3624
[56] [57] Xie F, Lin W T, Lin Y H, Mo J Q 2011 Chin. Phys. B 20 010208.
[58] He J H 2002 Approximate Analytical Methods in Engineering and Sciences (Zhengzhou: Henan Science and Technology Press) (in Chinese)[何吉欢 2002 工程和科学计算中的近似分析方法 (郑州: 河南科学技术出版社)]
[59] [60] [61] Chou J F 2002 Nonlinear and complexity in Atmospheric Sciences (Beijing: China Meteorological Press) (in Chineae)[丑纪范 2002 大气科学中的非线性与复杂性 (北京: 气象出版社)]
[62] Jordan D W, Smith P 1977 Nonlinear Ordinary Differential Equations (Oxford: Oxford University Press)
[63]
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