扰动Vakhnenko方程物理模型的行波解

莫嘉琪

doi:10.7498/aps.60.090203

摘要

研究了一类扰动Vakhnemko方程.给出了改进的渐近方法.首先, 对原模型系统对应的典型方程得到对应的行波解.其次, 引入一个泛函, 建立迭代关系式,将求解非线性问题转化为求解一系列的迭代序列.然后, 逐次地求出对应的解的近似式, 最后,得到了原扰动Vakhnemko模型行波解的任意次精度的近似展开式,并讨论了它的精度.

关键词:

泛函 /
行波解 /
Vakhnemko方程

A kind of disturbed Vakhnemko equation is considered. The modified asymptotic method is given. Firstly, we obtain corresponding traveling wave solution of the typical Vakhnemko equation. Secondly, introducing a functional, constructing the iteration expansion of solution, the nonlinear equation is converted into a set of iteration sequence. And then, the corresponding approximations of solution are solved successively. Finally, the approximate expansion for arbitrary order accuracy of the travelling wave solution for the original disturbed Vakhnemko model is obtained and its accuracy is discussed.

Keywords:

作者及机构信息

莫嘉琪

1.
安徽师范大学数学系,芜湖 241003;上海高校计算科学E-研究院SJTU研究所,上海 200240

基金项目: 国家自然科学基金(批准号:40876010), 中国科学院知识创新工程重要方向项目(批准号:KZCX2-YW-Q03-08), 公益性行业科研专项(批准号:GYHY200806010), LASG国家重点实验室专项经费, 上海市教育委员会E-研究院建设计划项目(批准号:E03004),浙江省自然科学基金(批准号:Y6110502)和安徽高校省级自然科学研究项目(批准号:KJ2011A135)资助的课题.

Authors and contacts

Mo Jia-Qi

1.
Department of Mathematics, Anhui Normal University, Wuhu 241003, China;Institute of Medical Imaging Technology, University of Shanghai Science and Technology, Shanghai 200093, China;Division of Computational Science, E-Institutes of Shanghai Universities at SJTU, Shanghai 200240,China

参考文献

[1]	McPhaden M J, Zhang D 2002 Nature 415 603
[2]	Gu D F, Philander S G H 1997 Science 275 805
[3]	Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [马松华、强继业、方建平 2007 物理学报 56 620]
[4]	Ma S H, Qiang, J Y, Fang J P 2007 Comm. Theor. Phys. 48 662
[5]	Loutsenko I 2006 Comm. Math. Phys. 268 465
[6]	Parkes E J 2008 Chaos Solitons Fractals 38 154
[7]	Li X Z, Wang M L 2007 Phys. Lett. A 361 115
[8]	Cheng X P, Lin J, Yao J M 2009 Chin. Phys. B 18 391
[9]	Sirendaoreji, Jiong S 2003 Phys. Lett. A 309 387
[10]	You F C, Zhang J, Hao H H 2009 Chin. Phys. Lett. 26 090201
[11]	Jia X Y, Wang N 2009 Chin. Phys. Lett. 26 080201
[12]	Chen C, Zhou Z X 2009 Chin. Phys. Lett. 26 080504
[13]	Huang D J, Mei J Q, Zhang H Q 2009 Chin. Phys. Lett. 26 050202
[14]	Jiao X Y, Yao R X, Lou S Y 2009 Chin. Phys. Lett. 26 040202
[15]	Pan L X, Zuo W M, Yan J R 2005 Acta Phys. Sin. 54 1 (in Chinese)[潘留仙、左伟明、颜家壬 2005 物理学报 54 1]
[16]	Li W A, Chen H, Zhang G C 2009 Chin. Phys. B 18 400
[17]	He J H, Wu X H 2006 Chaos, Solitions & Fractals 29 108
[18]	Ni W M, Wei J C 2006 J. Differ. Equations 221 158
[19]	Bartier J P 2006 Asymptotic Anal. 46 325
[20]	Libre J, da Silva P R, Teixeira M A 2007 J. Dyn. Differ. Equations 19 309
[21]	Guarguaglini F R, Natalini R 2007 Commun. Partial Differ. Equations 32 163
[22]	Mo J Q, Lin W T J. Sys. Sci. & Complexity 20 119
[23]	Mo J Q, 2010 Chin. Phys. B 19 010203
[24]	Mo J Q, Wang H 2007 Acta Ecologica Sinica 27 4366
[25]	Mo J Q, Zhu J, Wang H 2003 Prog. Nat. Sci. 13 768
[26]	Mo J Q 2009 Chin. Phys. Lett. 26 010204
[27]	Mo J Q 2009 Chin Phys. Lett. 26 060202
[28]	Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[29]	Mo J Q, Chen X F 2010 Acta Phys. Sin. 59 2919 (in Chinese) [莫嘉琪、陈贤峰 2010 物理学报 59 2919]
[30]	Mo J Q 2009 Science in China G 39 568
[31]	Mo J Q, Lin W T, Wang H 2008 Chin. Geographical Sci. 18 193
[32]	Mo J Q, Lin W T, Wang H 2007 Prog. Nat. Sci. 17 230
[33]	Mo J Q, Lin Y H, Lin W T 2009 Acta Phys. Sin. 58 6692 (in Chinese) [莫嘉琪、林一骅、林万涛 2009 物理学报 58 6692]
[34]	Mo J Q, Lin W T, Lin Y H 2007 Acta Phys. Sin. 56 3127 (in Chinese)[莫嘉琪、林万涛、林一骅 2007 物理学报 56 3127]
[35]	Mo J Q, Lin W T, Wang H 2009 Acta Math. Sci. 29B 101
[36]	Mo J Q, Lin W T, Wang H 2007 Chin. Phys. 16 951
[37]	Mo J Q, Lin W T 2008 Chin. Phys. B 17 370
[38]	Mo J Q, Lin W T 2008 Chin. Phys. B 17 743
[39]	Mo J Q, Lin W T, Lin Y H 2009 Chin. Phys. B 18 3624
[40]	Haraux A 181. Nonlinear Evolution Equation-Global Behavior of Solution (Lecture Notes in Mathemstics 841 Berlin: Springer-Verlager)
[41]	de Jager E M, JiangFuru 1996 The Theory of Singular Perturbation (Amsterdam: North- Holland Publishing)

施引文献

[1]	McPhaden M J, Zhang D 2002 Nature 415 603
[2]	Gu D F, Philander S G H 1997 Science 275 805
[3]	Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [马松华、强继业、方建平 2007 物理学报 56 620]
[4]	Ma S H, Qiang, J Y, Fang J P 2007 Comm. Theor. Phys. 48 662
[5]	Loutsenko I 2006 Comm. Math. Phys. 268 465
[6]	Parkes E J 2008 Chaos Solitons Fractals 38 154
[7]	Li X Z, Wang M L 2007 Phys. Lett. A 361 115
[8]	Cheng X P, Lin J, Yao J M 2009 Chin. Phys. B 18 391
[9]	Sirendaoreji, Jiong S 2003 Phys. Lett. A 309 387
[10]	You F C, Zhang J, Hao H H 2009 Chin. Phys. Lett. 26 090201
[11]	Jia X Y, Wang N 2009 Chin. Phys. Lett. 26 080201
[12]	Chen C, Zhou Z X 2009 Chin. Phys. Lett. 26 080504
[13]	Huang D J, Mei J Q, Zhang H Q 2009 Chin. Phys. Lett. 26 050202
[14]	Jiao X Y, Yao R X, Lou S Y 2009 Chin. Phys. Lett. 26 040202
[15]	Pan L X, Zuo W M, Yan J R 2005 Acta Phys. Sin. 54 1 (in Chinese)[潘留仙、左伟明、颜家壬 2005 物理学报 54 1]
[16]	Li W A, Chen H, Zhang G C 2009 Chin. Phys. B 18 400
[17]	He J H, Wu X H 2006 Chaos, Solitions & Fractals 29 108
[18]	Ni W M, Wei J C 2006 J. Differ. Equations 221 158
[19]	Bartier J P 2006 Asymptotic Anal. 46 325
[20]	Libre J, da Silva P R, Teixeira M A 2007 J. Dyn. Differ. Equations 19 309
[21]	Guarguaglini F R, Natalini R 2007 Commun. Partial Differ. Equations 32 163
[22]	Mo J Q, Lin W T J. Sys. Sci. & Complexity 20 119
[23]	Mo J Q, 2010 Chin. Phys. B 19 010203
[24]	Mo J Q, Wang H 2007 Acta Ecologica Sinica 27 4366
[25]	Mo J Q, Zhu J, Wang H 2003 Prog. Nat. Sci. 13 768
[26]	Mo J Q 2009 Chin. Phys. Lett. 26 010204
[27]	Mo J Q 2009 Chin Phys. Lett. 26 060202
[28]	Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys. B 19 030202
[29]	Mo J Q, Chen X F 2010 Acta Phys. Sin. 59 2919 (in Chinese) [莫嘉琪、陈贤峰 2010 物理学报 59 2919]
[30]	Mo J Q 2009 Science in China G 39 568
[31]	Mo J Q, Lin W T, Wang H 2008 Chin. Geographical Sci. 18 193
[32]	Mo J Q, Lin W T, Wang H 2007 Prog. Nat. Sci. 17 230
[33]	Mo J Q, Lin Y H, Lin W T 2009 Acta Phys. Sin. 58 6692 (in Chinese) [莫嘉琪、林一骅、林万涛 2009 物理学报 58 6692]
[34]	Mo J Q, Lin W T, Lin Y H 2007 Acta Phys. Sin. 56 3127 (in Chinese)[莫嘉琪、林万涛、林一骅 2007 物理学报 56 3127]
[35]	Mo J Q, Lin W T, Wang H 2009 Acta Math. Sci. 29B 101
[36]	Mo J Q, Lin W T, Wang H 2007 Chin. Phys. 16 951
[37]	Mo J Q, Lin W T 2008 Chin. Phys. B 17 370
[38]	Mo J Q, Lin W T 2008 Chin. Phys. B 17 743
[39]	Mo J Q, Lin W T, Lin Y H 2009 Chin. Phys. B 18 3624
[40]	Haraux A 181. Nonlinear Evolution Equation-Global Behavior of Solution (Lecture Notes in Mathemstics 841 Berlin: Springer-Verlager)
[41]	de Jager E M, JiangFuru 1996 The Theory of Singular Perturbation (Amsterdam: North- Holland Publishing)

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PDF下载量: 534
被引次数: 0

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