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Travelling wave solution of disturbed Vakhnenko equation for physical model

Mo Jia-Qi

Travelling wave solution of disturbed Vakhnenko equation for physical model

Mo Jia-Qi
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  • 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.
    • Funds:
    [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)

  • [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)

  • [1] Simulation of the nonlinear cahn-hilliard equation based onthe local refinement pure meshless method. Acta Physica Sinica, 2020, (): . doi: 10.7498/aps.69.20191829
    [2] Wang Jing-Li, Chen Zi-Yu, Chen He-Ming. Design of polarization-insensitive 1 × 2 multimode interference demultiplexer based on Si3N4/SiNx/Si3N4 sandwiched structure. Acta Physica Sinica, 2020, 69(5): 054206. doi: 10.7498/aps.69.20191449
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Publishing process
  • Received Date:  14 November 2010
  • Accepted Date:  03 December 2010
  • Published Online:  15 September 2011

Travelling wave solution of disturbed Vakhnenko equation for physical model

  • 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

Abstract: 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.

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