一类广义扰动KdV-Burgers方程的同伦近似解

洪宝剑; 卢殿臣

doi:10.7498/aps.62.170202

摘要

通过构造一个同伦映射, 研究了一类广义扰动KdV-Burgers方程. 在引入典型无扰动任意次广义KdV-Burgers方程扭状孤立波解的基础上, 研究了扰动方程的具有任意精度的近似解,指出了近似解级数的收敛性, 最后利用不动点定理,进一步说明近似解的有效性,并对精度进行了讨论.

关键词:

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.

Keywords:

generalized disturbed KdV-Burgers equation /
homotopy mapping /
asymptotic method /
approximate solution

作者及机构信息

洪宝剑^1,2,
卢殿臣¹

1.
江苏大学理学院, 镇江 212013;

2.
南京工程学院数理部, 南京 211167

基金项目: 国家自然科学基金(批准号: 61070231);江苏省六大人才高峰杰出个人基金(批准号: 2009188);江苏省研究生培养创新工程基金(批准号: CXLX13673)和南京工程学院创新基金(批准号: CKJB201218)资助的课题.

Authors and contacts

1.
Faculty of Science, Jiangsu University, Zhenjiang 212013, China;

2.
Department of mathematical and physical science, Nanjing Institute of Technology, Nanjing 211167, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61070231), the Outstanding Personal Program in Six Fields of Jiangsu Province, China (Grant No. 2009188), the Graduate Student Innovation Project of Jiangsu Province, China (Grant No. CXLX13_673), and the General Program of Innovation Foundation of NanJing Institute of Technology, China (Grant No. CKJB201218).

参考文献

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[2]	Fan E G 2000 Phys. Lett. A 265 353
[3]	Hong B J 2009 Appl. Math. Comput. 215 2908
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[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 57 5384]
[12]	Li R Q, Li C B 2002 Acta Phys. Sin. 51 1743 (in Chinese) [李睿劬, 李存标 2002 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 55 1555]
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[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 62 010201]
[18]	Wu Q K 2011 Acta Phys. Sin. 60 068802 (in Chinese) [吴钦宽 2011 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 60 030207]
[20]	Naranmandula, Han Y C 2010 Acta Phys. Sin. 59 2942 (in Chinese) [那仁满都拉, 韩元春 2010 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 60 020402]
[22]	Pan J T, Gong L X 2007 Acta Phys. Sin. 56 5585 (in Chinese) [潘军廷, 龚伦训 2007 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 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 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)

施引文献

[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 61 060501]
[5]	Mo J Q 2011 Acta Phys. Sin. 60 020202 (in Chinese) [莫嘉琪 2011 60 020202]
[6]	Wu Q K 2005 Acta Phys. Sin. 54 2510 (in Chinese) [吴钦宽 2005 54 2510]
[7]	Tang R R 2012 Acta Phys. Sin. 61 200201 (in Chinese) [唐荣荣 2012 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 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 57 5384]
[12]	Li R Q, Li C B 2002 Acta Phys. Sin. 51 1743 (in Chinese) [李睿劬, 李存标 2002 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 55 1555]
[14]	Shi Y R, Yang H J 2010 Acta Phys. Sin. 59 0067 (in Chinese) [石玉仁, 杨红娟 2010 59 0067]
[15]	Mo J Q, Yao J S 2008 Acta Phys. Sin. 57 7419 (in Chinese) [莫嘉琪, 姚静荪 2008 57 7419]
[16]	Shi L F, Mo J Q 2009 Acta Phys. Sin. 58 8123 (in Chinese) [石兰芳, 莫嘉琪 2009 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 62 010201]
[18]	Wu Q K 2011 Acta Phys. Sin. 60 068802 (in Chinese) [吴钦宽 2011 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 60 030207]
[20]	Naranmandula, Han Y C 2010 Acta Phys. Sin. 59 2942 (in Chinese) [那仁满都拉, 韩元春 2010 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 60 020402]
[22]	Pan J T, Gong L X 2007 Acta Phys. Sin. 56 5585 (in Chinese) [潘军廷, 龚伦训 2007 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 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 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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