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A class of generalized disturbed KdV-Burgers equation is studied by constructing a homotopy mapping. Based on the kinked solitary-wave solution of the corresponding typical undisturbed generalized KdV-Burgers equation with nonlinear terms of any order,the approximate solution with arbitrary degree of accuracy for the disturbed equation is researched. It is pointed out that the series of approximate solution is convergent. Finally,the efficiency and accuracy of the approximate solutions is also discussed by using the fixed point theorem.
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Keywords:
- generalized disturbed KdV-Burgers equation /
- homotopy mapping /
- asymptotic method /
- approximate solution
[1] Ablowitz M J, Clarkson P A 1991 Soliton, Nonlinear Evolution Equations and Inverse Scatting (New York: Cambridge University Press)
[2] Fan E G 2000 Phys. Lett. A 265 353
[3] Hong B J 2009 Appl. Math. Comput. 215 2908
[4] Ren A D, He X J, Wang X L, Zhang L X 2012 Acta Phys. Sin. 61 060501 (in Chinese) [任爱娣, 何学军, 王晓林, 张良欣 2012 物理学报 61 060501]
[5] Mo J Q 2011 Acta Phys. Sin. 60 020202 (in Chinese) [莫嘉琪 2011 物理学报 60 020202]
[6] Wu Q K 2005 Acta Phys. Sin. 54 2510 (in Chinese) [吴钦宽 2005 物理学报 54 2510]
[7] Tang R R 2012 Acta Phys. Sin. 61 200201 (in Chinese) [唐荣荣 2012 物理学报 61 200201]
[8] Fu H S, Cao L, Han B 2004 Chinese J. Geophys. 55 2173 (in Chinese) [傅红笋, 曹莉, 韩波 2004 地球物理学报 55 2173]
[9] Liao S J 2009 Commun Nonlinear Sci Numer Simulat. 14 983
[10] Mo J Q, Chen X F 2010 Chin. Phys. B 19 100203
[11] Zhang Q C, Wang W, He X J 2008 Acta Phys. Sin. 57 5384 (in Chinese) [张琪昌, 王炜, 何学军 2008 物理学报 57 5384]
[12] Li R Q, Li C B 2002 Acta Phys. Sin. 51 1743 (in Chinese) [李睿劬, 李存标 2002 物理学报 51 1743]
[13] Shi Y R, Xu X J, Wu Z X 2006 Acta Phys. Sin. 55 1555 (in Chinese) [石玉仁, 许新建, 吴枝喜 2006 物理学报 55 1555]
[14] Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 0067 (in Chinese) [石玉仁, 杨红娟 2010 物理学报 59 0067]
[15] Mo J Q, Yao J S 2008 Acta Phys. Sin. 57 7419 (in Chinese) [莫嘉琪, 姚静荪 2008 物理学报 57 7419]
[16] Shi L F, Mo J Q 2009 Acta Phys. Sin. 58 8123 (in Chinese) [石兰芳, 莫嘉琪 2009 物理学报 58 8123]
[17] 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 物理学报 62 010201]
[18] Wu Q K 2011 Acta Phys. Sin. 60 068802 (in Chinese) [吴钦宽 2011 物理学报 60 068802]
[19] Ye W C, Li B, Wang J 2011 Acta Phys. Sin. 60 030207 (in Chinese) [叶望川, 李彪, 王佳 2011 物理学报 60 030207]
[20] Naranmandula, Han Y C 2010 Acta Phys. Sin. 59 2942 (in Chinese) [那仁满都拉, 韩元春 2010 物理学报 59 2942]
[21] Shi Y R, Zhang J, Yang H J, Duan W S 2011 Acta Phys. Sin. 60 020402 (in Chinese) [石玉仁, 张娟, 杨红娟, 段文山 2011 物理学报 60 020402]
[22] Pan J T, Gong L X 2007 Acta Phys. Sin. 56 5585 (in Chinese) [潘军廷, 龚伦训 2007 物理学报 56 5585]
[23] Lu D C, Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617 (in Chinese) [卢殿臣, 洪宝剑, 田立新 2006 物理学报 55 5617]
[24] L K P, Shi Y R, Duan W S, Zhao J B 2001 Acta Phys. Sin. 50 2073 (in Chinese) [吕克璞, 石玉仁, 段文山, 赵金保 2001 物理学报 50 2073]
[25] Luwai W 2009 Commun Nonlinear Sci Numer Simul. 14 443
[26] Zhang W G, Chang Q S, Jiang B G 2002 Chaos, Solitons and Fractals 13 311
[27] Doğan Kaya 2004 Appl. Math. Comput. 152 709
[28] Wang J 2010 Appl. Math. Comput. 217 1652
[29] Hassan M M 2004 Chaos, Solitons and Fractals 19 1201
[30] Li B, Chen Y, Zhang H Q 2003 Chaos, Solitons and Fractals 15 647
[31] Liao S J 2004 Beyond Perturbati on: Introduction to the Homotopy Analysis Method (New York: CRC Press)
[32] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
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[1] Ablowitz M J, Clarkson P A 1991 Soliton, Nonlinear Evolution Equations and Inverse Scatting (New York: Cambridge University Press)
[2] Fan E G 2000 Phys. Lett. A 265 353
[3] Hong B J 2009 Appl. Math. Comput. 215 2908
[4] Ren A D, He X J, Wang X L, Zhang L X 2012 Acta Phys. Sin. 61 060501 (in Chinese) [任爱娣, 何学军, 王晓林, 张良欣 2012 物理学报 61 060501]
[5] Mo J Q 2011 Acta Phys. Sin. 60 020202 (in Chinese) [莫嘉琪 2011 物理学报 60 020202]
[6] Wu Q K 2005 Acta Phys. Sin. 54 2510 (in Chinese) [吴钦宽 2005 物理学报 54 2510]
[7] Tang R R 2012 Acta Phys. Sin. 61 200201 (in Chinese) [唐荣荣 2012 物理学报 61 200201]
[8] Fu H S, Cao L, Han B 2004 Chinese J. Geophys. 55 2173 (in Chinese) [傅红笋, 曹莉, 韩波 2004 地球物理学报 55 2173]
[9] Liao S J 2009 Commun Nonlinear Sci Numer Simulat. 14 983
[10] Mo J Q, Chen X F 2010 Chin. Phys. B 19 100203
[11] Zhang Q C, Wang W, He X J 2008 Acta Phys. Sin. 57 5384 (in Chinese) [张琪昌, 王炜, 何学军 2008 物理学报 57 5384]
[12] Li R Q, Li C B 2002 Acta Phys. Sin. 51 1743 (in Chinese) [李睿劬, 李存标 2002 物理学报 51 1743]
[13] Shi Y R, Xu X J, Wu Z X 2006 Acta Phys. Sin. 55 1555 (in Chinese) [石玉仁, 许新建, 吴枝喜 2006 物理学报 55 1555]
[14] Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 0067 (in Chinese) [石玉仁, 杨红娟 2010 物理学报 59 0067]
[15] Mo J Q, Yao J S 2008 Acta Phys. Sin. 57 7419 (in Chinese) [莫嘉琪, 姚静荪 2008 物理学报 57 7419]
[16] Shi L F, Mo J Q 2009 Acta Phys. Sin. 58 8123 (in Chinese) [石兰芳, 莫嘉琪 2009 物理学报 58 8123]
[17] 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 物理学报 62 010201]
[18] Wu Q K 2011 Acta Phys. Sin. 60 068802 (in Chinese) [吴钦宽 2011 物理学报 60 068802]
[19] Ye W C, Li B, Wang J 2011 Acta Phys. Sin. 60 030207 (in Chinese) [叶望川, 李彪, 王佳 2011 物理学报 60 030207]
[20] Naranmandula, Han Y C 2010 Acta Phys. Sin. 59 2942 (in Chinese) [那仁满都拉, 韩元春 2010 物理学报 59 2942]
[21] Shi Y R, Zhang J, Yang H J, Duan W S 2011 Acta Phys. Sin. 60 020402 (in Chinese) [石玉仁, 张娟, 杨红娟, 段文山 2011 物理学报 60 020402]
[22] Pan J T, Gong L X 2007 Acta Phys. Sin. 56 5585 (in Chinese) [潘军廷, 龚伦训 2007 物理学报 56 5585]
[23] Lu D C, Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617 (in Chinese) [卢殿臣, 洪宝剑, 田立新 2006 物理学报 55 5617]
[24] L K P, Shi Y R, Duan W S, Zhao J B 2001 Acta Phys. Sin. 50 2073 (in Chinese) [吕克璞, 石玉仁, 段文山, 赵金保 2001 物理学报 50 2073]
[25] Luwai W 2009 Commun Nonlinear Sci Numer Simul. 14 443
[26] Zhang W G, Chang Q S, Jiang B G 2002 Chaos, Solitons and Fractals 13 311
[27] Doğan Kaya 2004 Appl. Math. Comput. 152 709
[28] Wang J 2010 Appl. Math. Comput. 217 1652
[29] Hassan M M 2004 Chaos, Solitons and Fractals 19 1201
[30] Li B, Chen Y, Zhang H Q 2003 Chaos, Solitons and Fractals 15 647
[31] Liao S J 2004 Beyond Perturbati on: Introduction to the Homotopy Analysis Method (New York: CRC Press)
[32] Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)
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