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In this paper, we create an asymptotic method of solving the nonlinear equation for the sea-air oscillator model. And based on a class of oscillator of the sea-air oscillator model. We first expanding the time delay, then discussing the relative values for the small parameters in the case of three copies, and finally, obtain uniformly valid asymptotic expansion by using the theory of the differential inequity.
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Keywords:
- nonlinear /
- approximate method /
- small perturbation
[1] 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]
[2] 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]
[3] Li C G 2003 Acta Phys. Sin. 52 2114 (in Chinese) [李春贵 2003 52 2114]
[4] Li Z, Han C Z 2002 Chin. Phys. 11 9
[5] Lin J, Xu Y S 2003 Chin. Phys. 12 1049
[6] Hu Y Q 2002 Introductory to Atmospheric Thermodynamics and Dynamics–Linear and Nonlinear Thermodynamics of the Atmospheric Non-equilibrium State (Beijng: 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)]
[7] Jin F F 1997 J. Armos. Sci. 54 811
[8] Li X J, Chen X Q, Yan J 2013 Acta Phys. Sin. 62 160202 (in Chinese) [李晓静, 陈绚青, 严静 2013 62 160202]
[9] Li X J 2010 Chin. Phys. B 19 030201
[10] Wang C 2001 J. Adv. Atmosph. Sci. 18 674
[11] Zhao Q, Liu S K, Liu S D 2012 Acta Phys. Sin. 61 220201 (in Chinese) [赵强, 刘式适, 刘式达 2012 61 220201]
[12] Liu S K, Liu S D 2012 Nonlinear Equations in Physics (Beijing: Peking University Press) (in China) [刘式适, 刘式达 2012 物理学中的非线性方程 (北京: 北京大学出版社)]
[13] de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co)
[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] Lin W T, Ji Z Z, Wang B 2001 Prog. Nat. Sci. 12 102 (in Chinese) [林万涛, 季仲贞, 王斌 2002 自然科学进展 12 102]
[19] Lin W T, Mo J Q 2003 Chin. Sci. Bull. 48 suppl. II 5
[20] Lin W T, Lin Y H, Mo J Q 2012 Chin. Phys. B 21 010204
[21] Han X L, Zhao Z J, Cheng E J, Mo J Q 2013 Acta Phys. Sin. 62 110202 (in Chinese) [韩祥临,赵振江, 程荣军, 莫嘉琪 2013 62 110202]
[22] Han X L, Du Z J, Mo J Q 2012 Acta Phys. Sin. 61 200208 (in Chinese) [韩祥临, 杜增吉, 莫嘉琪 2012 61 200208]
[23] Shi L F, Ouyang C, Chen L H, Mo J Q 2012 Acta Phys. Sin. 61 050203 (in Chinese) [石兰芳, 欧阳成, 陈丽华, 莫嘉琪 2012 61 050203]
[24] Shi L F, Lin W T, Lin Y H, Mo J Q 2013 Acta Phys. Sin. 62 010201 (in Chinese) [石兰芳, 林万涛, 林一骅, 莫嘉琪 2013 62 010201]
[25] Mo J Q, Lin Y H, Lin W T, Chen L H 2012 Chin. Geog. Sci. 22 42
[26] Mo J Q 2009 Sci. China G 39 568
[27] 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]
[28] Mo J Q 2011 Acta Phys. Sin. 60 090203 (in Chinese) [莫嘉琪 2011 60 090203]
[29] Mo J Q 2011 Commun. Theor. Phys. 53 440
[30] Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 070205
[31] Chang K W, Howes F A 1984 Nonlinear Singular Perturbation Phenomena: Theory and Applications (New York: Springer-Verlag)
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[1] 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]
[2] 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]
[3] Li C G 2003 Acta Phys. Sin. 52 2114 (in Chinese) [李春贵 2003 52 2114]
[4] Li Z, Han C Z 2002 Chin. Phys. 11 9
[5] Lin J, Xu Y S 2003 Chin. Phys. 12 1049
[6] Hu Y Q 2002 Introductory to Atmospheric Thermodynamics and Dynamics–Linear and Nonlinear Thermodynamics of the Atmospheric Non-equilibrium State (Beijng: 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)]
[7] Jin F F 1997 J. Armos. Sci. 54 811
[8] Li X J, Chen X Q, Yan J 2013 Acta Phys. Sin. 62 160202 (in Chinese) [李晓静, 陈绚青, 严静 2013 62 160202]
[9] Li X J 2010 Chin. Phys. B 19 030201
[10] Wang C 2001 J. Adv. Atmosph. Sci. 18 674
[11] Zhao Q, Liu S K, Liu S D 2012 Acta Phys. Sin. 61 220201 (in Chinese) [赵强, 刘式适, 刘式达 2012 61 220201]
[12] Liu S K, Liu S D 2012 Nonlinear Equations in Physics (Beijing: Peking University Press) (in China) [刘式适, 刘式达 2012 物理学中的非线性方程 (北京: 北京大学出版社)]
[13] de Jager E M, Jiang F R 1996 The Theory of Singular Perturbation (Amsterdam: North-Holland Publishing Co)
[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] Lin W T, Ji Z Z, Wang B 2001 Prog. Nat. Sci. 12 102 (in Chinese) [林万涛, 季仲贞, 王斌 2002 自然科学进展 12 102]
[19] Lin W T, Mo J Q 2003 Chin. Sci. Bull. 48 suppl. II 5
[20] Lin W T, Lin Y H, Mo J Q 2012 Chin. Phys. B 21 010204
[21] Han X L, Zhao Z J, Cheng E J, Mo J Q 2013 Acta Phys. Sin. 62 110202 (in Chinese) [韩祥临,赵振江, 程荣军, 莫嘉琪 2013 62 110202]
[22] Han X L, Du Z J, Mo J Q 2012 Acta Phys. Sin. 61 200208 (in Chinese) [韩祥临, 杜增吉, 莫嘉琪 2012 61 200208]
[23] Shi L F, Ouyang C, Chen L H, Mo J Q 2012 Acta Phys. Sin. 61 050203 (in Chinese) [石兰芳, 欧阳成, 陈丽华, 莫嘉琪 2012 61 050203]
[24] Shi L F, Lin W T, Lin Y H, Mo J Q 2013 Acta Phys. Sin. 62 010201 (in Chinese) [石兰芳, 林万涛, 林一骅, 莫嘉琪 2013 62 010201]
[25] Mo J Q, Lin Y H, Lin W T, Chen L H 2012 Chin. Geog. Sci. 22 42
[26] Mo J Q 2009 Sci. China G 39 568
[27] 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]
[28] Mo J Q 2011 Acta Phys. Sin. 60 090203 (in Chinese) [莫嘉琪 2011 60 090203]
[29] Mo J Q 2011 Commun. Theor. Phys. 53 440
[30] Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 070205
[31] Chang K W, Howes F A 1984 Nonlinear Singular Perturbation Phenomena: Theory and Applications (New York: Springer-Verlag)
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