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The EI Ni o/La Ni a and the Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific Ocean-atmosphere interactions. This paper, aims at creating an approximate solving method of nonlinear equation for the ENSO models. And based on a class of oscillator of ENSO models, employing the method of homotopic mapping, the approximate and exact solutions of the corresponding problem is studied. The accuracy of approximate solution is discussed. It is proved from the results that homotopic method can be used for analyzing the SST anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.
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Keywords:
- nonlinear /
- homotopy mapping /
- perturbation /
- ENSO model
[1] Bjerknes J A 1996 Tellus. 18 820
[2] McCreary J P, Anderson D L T 1984 Mon. Wea. Rev. 112 934
[3] Cane M A, Zebiak S E 1985 228 1084
[4] Anderson D L T, McCreary J P 1985 J. Atmos. Sci. 42 615
[5] Zebiak S E, Cane M A 1987 Mon. Wea. Rev. 115 2262
[6] Schopf P S, Suarez M J 1988 J. Atmos. Sci. 45 549
[7] Philander S G, Lau N C, Pacanowski R C 1989 Philos. Trans. Roy. Soc. London Ser. A 329 167
[8] Latif M, Sterl A, Maier-Reimer E 1993 J. Climate 6 700
[9] Neelin J D 1989 Philos. Trans. Roy. Soc. London Ser. A 329 189
[10] Neelin J D 1990 J. Atmos. Sci. 47 674
[11] Bjerknes J 1969 Mon. Wea. Rev. 97 163
[12] Neelin J D, Latif M, Jin F F 1994 Annu. Rev. Fluid Mech. 26 617
[13] McWilliams J C, Gent P R 1991 J. Atmos. Sci. 35 962
[14] Lau K M 1981 J. Atmos. Sci. 38 248
[15] McCreary J P 1983 Mon. Wea. Rev. 111 370
[16] Philander S G. H, Yamagata T, Pacanowski R C 1984 J. Atmos. Sci. 41 604
[17] Gill A E 1985 Elsevier Oceanography Series 40 303
[18] Yamagata T 1985 Elsevier Oceanography Series 40 637
[19] Hirst A C 1986 J. Atmos. Sci. 43 606
[20] Xie S P, Kubikawa A, Hanawa K 1989 J. Climate 2 946
[21] Wakata, Y, Sarachik E S 1991 J. Atmos .Sci. 48 2060
[22] Jin F F, Neelin J D 1993 J. Atmos. Sci. 50 3523
[23] Jin F F, Neelin J D, Ghil M 1994 Science 264 70
[24] Wang C, Weisberg R H, Virmani J I 1999 J. Geophys. Res. 104 5131
[25] Wang B, Wang Y 1996 J. Climate 9 1586
[26] Cane M A, Munnich M, Zebiak S E 1990 J. Atmos. Sci. 47 1562
[27] Wang B, Fang Z 1996 J. Atmos. Sci. 53 2786
[28] Wang B, Barcilon A, Fang Z 1999 J. Atmos. Sci. 56 5
[29] Dai XG, Wang A H, Chou J F 2001 Chin. Phys. Sin. 50 606 (in Chinese) [戴新刚、王爱慧、丑纪范 2001 50 606]
[30] Feng G L, Dong W J, Jia X J 2002 Chin. Phys. Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静、曹鸿兴 2002 51 1181]
[31] Liu S K, Fu Z T, Liu S D 2002 Chin. Phys. Sin. 2002 51 10 (in Chinese) [刘式适、付遵涛、刘式达、赵 强 2002 51 10]
[32] Lin W T, Ji Z Z, Wag B 2003 Chinese Science Bulletin 48 999
[33] Lin W T, Mo J Q 2003 Chinese Science Bulletin 48(Ⅱ) 5
[34] Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 996 (in Chinese) [莫嘉琪、林万涛 2004 53 996]
[35] Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 996 (in Chinese) [莫嘉琪、林万涛 2004 53 996]
[36] Mo J Q, Lin W T 2005 Chin. Phys. 14 875
[37] Mo J Q, Lin W T, Wang H 2009 Acta Math. Sin. 29 101 (in Chinese) [莫嘉琪、林万涛 2009 59 101]
[38] Mo J Q, Lin W T 2008 Chin. Phys. B 17 370
[39] Mo J Q, Lin W T 2008 Chin. Phys. B 17 743
[40] de Jager E M, Jiang F 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co)
[41] Sagon G 2008 Nonlinearity 21 1183
[42] Hovhannisyan G, Vulanovic 2008 Nonlinear Stud. 15 297
[43] Barbu L, Cosma 2009 J. Math. Anal. Appl. 351 392
[44] Ramos M 2009 J. Math. Anal. Appl. 352 246
[45] Mo J Q, Zhang W J, He M 2007 Acta Phys. Sin. 56 1843 (in Chinese) [莫嘉琪、张伟江、何 铭 2007 56 1843]
[46] Mo J Q, Zhang W J, Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese) [莫嘉琪、张伟江、陈贤峰 2007 56 6689]
[47] Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese) [莫嘉琪 2009 58 695]
[48] Mo J Q, Yao J S 2009 Acta Phys. Sin. 58 7419 (in Chinese) [莫嘉琪、姚静荪 2009 58 7419]
[49] Mo J Q 2009 Acta Phys. Sin 58 2930 (in Chinese) [莫嘉琪 2008 58 2930]
[50] Mo J Q, Cheng Yan 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、陈 燕 2009 58 4379]
[51] Mo J Q 2009 Science in China,Ser. G 52 1007
[52] Mo J Q, Chen X F 2010 Acta Phys. Sin. 50 1403 (in Chinese) [莫嘉琪、 陈贤蜂 2010 501403]
[53] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys.B 19030202
[54] Mo J Q 2010 Chin. Phys. B 19 010203
[55] Liao S J, Chang A T 1998 ASME J.Appl. Mech. 65 914
[56] Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York: CRC Press Co)
[57] Jin F F 1997 J. Atmos. Sci. 54 811
[58] Wang C 2001 Advances in Atmospheric Sciences 18 674
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[1] Bjerknes J A 1996 Tellus. 18 820
[2] McCreary J P, Anderson D L T 1984 Mon. Wea. Rev. 112 934
[3] Cane M A, Zebiak S E 1985 228 1084
[4] Anderson D L T, McCreary J P 1985 J. Atmos. Sci. 42 615
[5] Zebiak S E, Cane M A 1987 Mon. Wea. Rev. 115 2262
[6] Schopf P S, Suarez M J 1988 J. Atmos. Sci. 45 549
[7] Philander S G, Lau N C, Pacanowski R C 1989 Philos. Trans. Roy. Soc. London Ser. A 329 167
[8] Latif M, Sterl A, Maier-Reimer E 1993 J. Climate 6 700
[9] Neelin J D 1989 Philos. Trans. Roy. Soc. London Ser. A 329 189
[10] Neelin J D 1990 J. Atmos. Sci. 47 674
[11] Bjerknes J 1969 Mon. Wea. Rev. 97 163
[12] Neelin J D, Latif M, Jin F F 1994 Annu. Rev. Fluid Mech. 26 617
[13] McWilliams J C, Gent P R 1991 J. Atmos. Sci. 35 962
[14] Lau K M 1981 J. Atmos. Sci. 38 248
[15] McCreary J P 1983 Mon. Wea. Rev. 111 370
[16] Philander S G. H, Yamagata T, Pacanowski R C 1984 J. Atmos. Sci. 41 604
[17] Gill A E 1985 Elsevier Oceanography Series 40 303
[18] Yamagata T 1985 Elsevier Oceanography Series 40 637
[19] Hirst A C 1986 J. Atmos. Sci. 43 606
[20] Xie S P, Kubikawa A, Hanawa K 1989 J. Climate 2 946
[21] Wakata, Y, Sarachik E S 1991 J. Atmos .Sci. 48 2060
[22] Jin F F, Neelin J D 1993 J. Atmos. Sci. 50 3523
[23] Jin F F, Neelin J D, Ghil M 1994 Science 264 70
[24] Wang C, Weisberg R H, Virmani J I 1999 J. Geophys. Res. 104 5131
[25] Wang B, Wang Y 1996 J. Climate 9 1586
[26] Cane M A, Munnich M, Zebiak S E 1990 J. Atmos. Sci. 47 1562
[27] Wang B, Fang Z 1996 J. Atmos. Sci. 53 2786
[28] Wang B, Barcilon A, Fang Z 1999 J. Atmos. Sci. 56 5
[29] Dai XG, Wang A H, Chou J F 2001 Chin. Phys. Sin. 50 606 (in Chinese) [戴新刚、王爱慧、丑纪范 2001 50 606]
[30] Feng G L, Dong W J, Jia X J 2002 Chin. Phys. Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静、曹鸿兴 2002 51 1181]
[31] Liu S K, Fu Z T, Liu S D 2002 Chin. Phys. Sin. 2002 51 10 (in Chinese) [刘式适、付遵涛、刘式达、赵 强 2002 51 10]
[32] Lin W T, Ji Z Z, Wag B 2003 Chinese Science Bulletin 48 999
[33] Lin W T, Mo J Q 2003 Chinese Science Bulletin 48(Ⅱ) 5
[34] Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 996 (in Chinese) [莫嘉琪、林万涛 2004 53 996]
[35] Mo J Q, Lin W T 2004 Acta Phys. Sin. 53 996 (in Chinese) [莫嘉琪、林万涛 2004 53 996]
[36] Mo J Q, Lin W T 2005 Chin. Phys. 14 875
[37] Mo J Q, Lin W T, Wang H 2009 Acta Math. Sin. 29 101 (in Chinese) [莫嘉琪、林万涛 2009 59 101]
[38] Mo J Q, Lin W T 2008 Chin. Phys. B 17 370
[39] Mo J Q, Lin W T 2008 Chin. Phys. B 17 743
[40] de Jager E M, Jiang F 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co)
[41] Sagon G 2008 Nonlinearity 21 1183
[42] Hovhannisyan G, Vulanovic 2008 Nonlinear Stud. 15 297
[43] Barbu L, Cosma 2009 J. Math. Anal. Appl. 351 392
[44] Ramos M 2009 J. Math. Anal. Appl. 352 246
[45] Mo J Q, Zhang W J, He M 2007 Acta Phys. Sin. 56 1843 (in Chinese) [莫嘉琪、张伟江、何 铭 2007 56 1843]
[46] Mo J Q, Zhang W J, Chen X F 2007 Acta Phys. Sin. 56 6169 (in Chinese) [莫嘉琪、张伟江、陈贤峰 2007 56 6689]
[47] Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese) [莫嘉琪 2009 58 695]
[48] Mo J Q, Yao J S 2009 Acta Phys. Sin. 58 7419 (in Chinese) [莫嘉琪、姚静荪 2009 58 7419]
[49] Mo J Q 2009 Acta Phys. Sin 58 2930 (in Chinese) [莫嘉琪 2008 58 2930]
[50] Mo J Q, Cheng Yan 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、陈 燕 2009 58 4379]
[51] Mo J Q 2009 Science in China,Ser. G 52 1007
[52] Mo J Q, Chen X F 2010 Acta Phys. Sin. 50 1403 (in Chinese) [莫嘉琪、 陈贤蜂 2010 501403]
[53] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys.B 19030202
[54] Mo J Q 2010 Chin. Phys. B 19 010203
[55] Liao S J, Chang A T 1998 ASME J.Appl. Mech. 65 914
[56] Liao S J 2004 Beyond Perturbation: Introduction to the Homotopy Analysis Method (New York: CRC Press Co)
[57] Jin F F 1997 J. Atmos. Sci. 54 811
[58] Wang C 2001 Advances in Atmospheric Sciences 18 674
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