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The EI Niño/La Niña and southern oscillation is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, the aim is to create a method of asymptotically solving the nonlinear singularly perturbed problem for the ocean-atmosphere oscillator models. And according to a class of ocean-atmosphere oscillator models, employing the singular perturbation method, we study the approximate solution of corresponding problem. The obtained results from singular perturbation method can be used for analyzing the sea surface temperature anomaly and the thermocline depth anomaly in the equatorial Pacific of the atmosphere-ocean oscillator for the EI Niño/La Niña and southern oscillation model.
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Keywords:
- nonlinear /
- approximate solution /
- El Niñ
[1] Jin F F 1997 J. Atmos. Sci. 54 811
[2] Jin F F 1997 J. Atmos. Sci. 54 830
[3] Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静, 曹鸿兴 2002 51 1181]
[4] Wang C 2001 1999 J. Adv. Atmosph. Sci. 18 674
[5] Guan X P, He Y H, Fan Z P 2003 Acta Phys. Sin. 52 276 (in Chinese) [关新平, 何宴辉, 范正平 2003 52 276]
[6] Li C G 2003 Acta Phys. Sin. 52 2114 (in Chinese) [李春贵 2003 52 2114]
[7] Li Z, Han C Z 2002 Chin. Phys. 11 9
[8] Lin J, Xu Y S 2003 Chin. Phys. 12 1049
[9] Wang B, Barcilon A, Fang Z 1999 J. Atmosp. Sci. 56 5
[10] Lin W T, Ji Z Z, Wang B, Yang X Z 2000 Chin. Sci. Bull. 45 1358
[11] Lin W T, Ji Z Z, Wang B 2002 Prog. Nat. Sci. 12 102 (in Chinese) [林万涛, 季仲贞, 王斌 2002 自然科学进展 12 102]
[12] Lin W T, Mo J Q 2004 Chin. Sci. Bull. 48 suppl. Ⅱ 5
[13] Hu Y Q 2002 Introductory to Atmospheric Thermodynamics and Dynamics-Linear and Nonlinear Thermodynamics of the Atmospheric Non-Equilibrium State (Beijing: Geology Pub.) (in Chinese) [胡隐樵 2002 大气热力动力学导论——大气非平衡态线性和非线性热力学 (北京:地质出版社)]
[14] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[15] Ramos M 2009 J. Math. Anal. Appl. 352 246
[16] D'Aprile T, Pistoia A 2010 J. Diff. Eqs. 248 556
[17] Faye L, Frenod E, Seck D 2011 Discrete Contin. Dyn. Sys. 29 1001
[18] Mo J Q 2009 Sci. China G 39 568
[19] 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 59 6701]
[20] Mo J Q, Lin W T, Lin Y H 2011 Acta Phys. Sin. 60 080202 (in Chinese) [莫嘉琪, 林万涛, 林一骅 2011 60 090202]
[21] Mo J Q 2011 Acta Phys. Sin. 60 090203 (in Chinese) [莫嘉琪 2011 60 090203]
[22] Mo J Q 2010 Commun. Theor. Phys. 53 440
[23] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[24] Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 070205
[25] Chang K W, Howes F A 1984 Nonlinear Singular Perturbation Phenomena: Theory and Applications, Applied Mathemaical Science (New York: Springer-Verlag) p56
[26] de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co.)
[27] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG.)
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[1] Jin F F 1997 J. Atmos. Sci. 54 811
[2] Jin F F 1997 J. Atmos. Sci. 54 830
[3] Feng G L, Dong W J, Jia X J, Cao H X 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静, 曹鸿兴 2002 51 1181]
[4] Wang C 2001 1999 J. Adv. Atmosph. Sci. 18 674
[5] Guan X P, He Y H, Fan Z P 2003 Acta Phys. Sin. 52 276 (in Chinese) [关新平, 何宴辉, 范正平 2003 52 276]
[6] Li C G 2003 Acta Phys. Sin. 52 2114 (in Chinese) [李春贵 2003 52 2114]
[7] Li Z, Han C Z 2002 Chin. Phys. 11 9
[8] Lin J, Xu Y S 2003 Chin. Phys. 12 1049
[9] Wang B, Barcilon A, Fang Z 1999 J. Atmosp. Sci. 56 5
[10] Lin W T, Ji Z Z, Wang B, Yang X Z 2000 Chin. Sci. Bull. 45 1358
[11] Lin W T, Ji Z Z, Wang B 2002 Prog. Nat. Sci. 12 102 (in Chinese) [林万涛, 季仲贞, 王斌 2002 自然科学进展 12 102]
[12] Lin W T, Mo J Q 2004 Chin. Sci. Bull. 48 suppl. Ⅱ 5
[13] Hu Y Q 2002 Introductory to Atmospheric Thermodynamics and Dynamics-Linear and Nonlinear Thermodynamics of the Atmospheric Non-Equilibrium State (Beijing: Geology Pub.) (in Chinese) [胡隐樵 2002 大气热力动力学导论——大气非平衡态线性和非线性热力学 (北京:地质出版社)]
[14] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
[15] Ramos M 2009 J. Math. Anal. Appl. 352 246
[16] D'Aprile T, Pistoia A 2010 J. Diff. Eqs. 248 556
[17] Faye L, Frenod E, Seck D 2011 Discrete Contin. Dyn. Sys. 29 1001
[18] Mo J Q 2009 Sci. China G 39 568
[19] 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 59 6701]
[20] Mo J Q, Lin W T, Lin Y H 2011 Acta Phys. Sin. 60 080202 (in Chinese) [莫嘉琪, 林万涛, 林一骅 2011 60 090202]
[21] Mo J Q 2011 Acta Phys. Sin. 60 090203 (in Chinese) [莫嘉琪 2011 60 090203]
[22] Mo J Q 2010 Commun. Theor. Phys. 53 440
[23] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[24] Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 070205
[25] Chang K W, Howes F A 1984 Nonlinear Singular Perturbation Phenomena: Theory and Applications, Applied Mathemaical Science (New York: Springer-Verlag) p56
[26] de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co.)
[27] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG.)
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