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Analytic approximation for the soliton solution of the discrete modified KdV equation

Yang Pei ,  Chen Yong ,  Li Zhi-Bin

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Analytic approximation for the soliton solution of the discrete modified KdV equation

Yang Pei, Chen Yong, Li Zhi-Bin
Acta Phys. Sin., 2010, 59(6): 3668-3673.
doi: 10.7498/aps.59.3668
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  • Abstract

    We extend the homotopy analysis method to solving the discrete modified KdV equation. The bright soliton solution expressed by a series of exponential functions is obtained, which agrees well with the exact solution. It indicates the validity and great potential of the homotopy analysis method in solving complicated nonlinear problems.

    Authors and contacts

    • (1)华东师范大学计算机科学技术系,上海 200241; (2)华东师范大学计算机科学技术系,上海 200241；华东师范大学上海市高可信计算重点实验室，上海 200062; (3)华东师范大学上海市高可信计算重点实验室，上海 200062

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    ［9］Ma W X, Hu X B, Zhu S M, Wu Y T 1999 J. Math. Phys. 40 6071
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    ］Zhang D J 2005 Chaos Solitons Fract. 23 1333
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    ］Sun Y P, Chen D Y, Xu X X 2006 Phys. Lett. A 359 47
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    ］Zhu J, Geng X 2007 Phys. Lett. A 368 464
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    ］Hu X B, Wu Y T 1998 Phys. Lett. A 246 523
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    ］Chou K S, Qu C Z 2001 Phys. Lett. A 280 303
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    ］Luo L, Fan E G 2007 Chin. Phys. Lett. 24 1444
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    ］Yang P, Chen Y, Li Z B 2008 Chin. Phys. B 17 3953
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    ］Zhang S Q 2007 Acta Phys. Sin. 56 1870 (in Chinese) ［张善卿 2007 56 1870］
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    ］Liu Y P, Li Z B 2009 J. Phys. A 42 125205
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    ］Liu Y P, Li Z B 2009 Chaos Solitons Fract. 39 1
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    ］Yang H J, Shi Y R, Duan W S，Lü K P 2007 Acta Phys. Sin. 56 3064 (in Chinese) ［杨红娟、石玉仁、段文山、吕克璞 2007 56 3064］
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    ］Shi Y R, Wang Y H, Yang H J, Duan W S 2007 Acta Phys. Sin. 56 6791 (in Chinese) ［石玉仁、汪映海、杨红娟、段文山 2007 56 6791］
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    ］Shi Y R, Xu X J, Wu Z X, Wang Y H, Yang H J, Duan W S, Lü K P 2006 Acta Phys. Sin. 55 1555 (in Chinese) ［石玉仁、许新建、吴枝喜、汪映海、杨红娟、段文山、吕克璞 2006 55 1555］
    [44]

    ］Xu W, Sun Z K, Yang X L 2005 Acta Phys. Sin. 54 5069 (in Chinese) ［徐伟、孙中奎、杨晓丽 2005 54 5069］
    [45]

    ］Wang Z, Zou L, Zhang H Q 2008 Commun. Theor. Phys. 49 1373
    [46]

    ］Zou L, Zong Z, Wang Z, He L 2007 Phys. Lett. A 370 287
  • [1]

    ［1］Fermi E, Pasta J, Ulam S 1965 Collected Papers of Enrico Fermi(Ⅱ) (Chicago: University of Chicago Press) p1
    [2]

    ［2］Suris Y B 1997 J. Phys. A 30 1745
    [3]

    ［3］Suris Y B 1999 Rev. Math. Phys. 11 727
    [4]

    ［4］Suris Y B 2003 The Problem of Integrable Discretization: Hamitonian Approach, Progress in Mathemetics ( Vol. 219) (Basel: Birkhuser-Verlag) p1
    [5]

    ［5］Blaszak M, Marciniak K 1994 J. Math. Phys. 35 4661
    [6]

    ［6］Belov A A, Chaltikian K D 1993 Phys. Lett. B 309 268
    [7]

    ［7］Hu X B, Zhu Z N 1998 J. Phys. A 31 4755
    [8]

    ［8］Hu X B, Zhu Z N 1998 J. Math. Phys. 39 4766
    [9]

    ［9］Ma W X, Hu X B, Zhu S M, Wu Y T 1999 J. Math. Phys. 40 6071
    [10]

    ］Zhang D J 2005 Chaos Solitons Fract. 23 1333
    [11]

    ］Sun Y P, Chen D Y, Xu X X 2006 Phys. Lett. A 359 47
    [12]

    ］Zhu J, Geng X 2007 Phys. Lett. A 368 464
    [13]

    ］Hu X B, Wu Y T 1998 Phys. Lett. A 246 523
    [14]

    ］Chou K S, Qu C Z 2001 Phys. Lett. A 280 303
    [15]

    ］Luo L, Fan E G 2007 Chin. Phys. Lett. 24 1444
    [16]

    ］Zhang W, Huang Y Z, Xiao Y 1998 Phys. Rev. E 57 7358
    [17]

    ］Xiao Y, Hai W H 1994 J. Phys. A 27 6873
    [18]

    ］Chow K W 1994 Phys. Scr. 50 233
    [19]

    ］Shek E C M, Chow K W 2008 Chaos Solitons Fract. 36 296
    [20]

    ］Yang P, Chen Y, Li Z B 2009 Appl. Math. Comput. 210 362
    [21]

    ］Yang P, Chen Y, Li Z B 2008 Chin. Phys. B 17 3953
    [22]

    ］Taogetusang, Sirendaoerji 2009 Acta Phys. Sin. 58 5894 (in Chinese) ［套格图桑、斯仁道尔吉 2009 58 5894］
    [23]

    ］Zhang S Q 2007 Acta Phys. Sin. 56 1870 (in Chinese) ［张善卿 2007 56 1870］
    [24]

    ］Liao S J 2003 Beyond Perturbation: Introduction to the Homotopy Analysis Method (Boca Raton: Chapman & Hall/CRC Press) p1
    [25]

    ］Liao S J 2002 J. Fluid Mech. 453 411
    [26]

    ］Liao S J 2003 Int. J. Non-Lin. Mech. 38 1173
    [27]

    ］Liao S J 2003 J. Fluid Mech. 488 189
    [28]

    ］Liao S J 2003 Appl. Math. Comput. 144 495
    [29]

    ］Liao S J 2004 Int. J. Non-Lin. Mech. 39 271
    [30]

    ］Liao S J 2004 Appl. Math. Comput. 147 499
    [31]

    ］Wu Y Y, Wang C, Liao S J 2005 Chaos Solitons Fract. 23 1733
    [32]

    ］Wu W, Liao S J 2005 Chaos Solitons Fract. 26 177
    [33]

    ］Liao S J 2009 Commun. Nonlin. Sci. Numer. Simulat. 14 983
    [34]

    ］Liao S J 2009 Commun. Nonlin. Sci. Numer. Simulat. 14 2144
    [35]

    ］Liao S J, Tan Y 2007 Stud. Appl. Math. 119 297
    [36]

    ］Abbasbandy S, Parkes E J 2008 Chaos Solitons Fract. 36 581
    [37]

    ］Abbasbandy S 2009 Chaos Solitons Fract. 39 428
    [38]

    ］Liu Y P, Li Z B 2008 Z. Naturforsch. A 63 241
    [39]

    ］Liu Y P, Li Z B 2009 J. Phys. A 42 125205
    [40]

    ］Liu Y P, Li Z B 2009 Chaos Solitons Fract. 39 1
    [41]

    ］Yang H J, Shi Y R, Duan W S，Lü K P 2007 Acta Phys. Sin. 56 3064 (in Chinese) ［杨红娟、石玉仁、段文山、吕克璞 2007 56 3064］
    [42]

    ］Shi Y R, Wang Y H, Yang H J, Duan W S 2007 Acta Phys. Sin. 56 6791 (in Chinese) ［石玉仁、汪映海、杨红娟、段文山 2007 56 6791］
    [43]

    ］Shi Y R, Xu X J, Wu Z X, Wang Y H, Yang H J, Duan W S, Lü K P 2006 Acta Phys. Sin. 55 1555 (in Chinese) ［石玉仁、许新建、吴枝喜、汪映海、杨红娟、段文山、吕克璞 2006 55 1555］
    [44]

    ］Xu W, Sun Z K, Yang X L 2005 Acta Phys. Sin. 54 5069 (in Chinese) ［徐伟、孙中奎、杨晓丽 2005 54 5069］
    [45]

    ］Wang Z, Zou L, Zhang H Q 2008 Commun. Theor. Phys. 49 1373
    [46]

    ］Zou L, Zong Z, Wang Z, He L 2007 Phys. Lett. A 370 287
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Publishing process
  • Received Date:  17 September 2009
  • Accepted Date:  03 December 2009
  • Published Online:  05 March 2010

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