LONG Yao, LI Ji-bin, RUI Wei-guo, HE Bin. Travelling Wave Solutions for a Hight Order Wave Equation of KdV Type[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1296-1306.
Citation: LONG Yao, LI Ji-bin, RUI Wei-guo, HE Bin. Travelling Wave Solutions for a Hight Order Wave Equation of KdV Type[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1296-1306.

Travelling Wave Solutions for a Hight Order Wave Equation of KdV Type

  • Received Date: 2006-02-28
  • Rev Recd Date: 2007-09-17
  • Publish Date: 2007-11-15
  • The theory of planar dynamical systems is used to study the dynamical behaviour of the travelling wave solutions of a nonlinear wave equations of KdV type. In different regions of the parametric space, sufficient conditions to guarantee the existence of solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions are given. All possible exact explicit parametric representations are obtained for these waves.
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  • [1]
    Tzirtzilakis E,Xenos M,Marinakis V,et al.Interactions and stability of solitary waves in shallow water[J].Chaos, Solitons and Fractals,2002,14(1):87-95. doi: 10.1016/S0960-0779(01)00211-9
    [2]
    Tzirtzilakis E,Marinakis V,Apokis C,et al.Soliton-like solutions of higher order wave equations of the Korteweg-de-Vries type[J].J Math Phys,2002,43(12):6151-6161. doi: 10.1063/1.1514387
    [3]
    Fokas A s.On a class of physically important integralequations[J].Physica D,1995,87(1/4):145-150. doi: 10.1016/0167-2789(95)00133-O
    [4]
    LONG Yao,RUI Wei-guo,HE Bin.Travelling wave solutions for a higher order wave equations of KdV type (Ⅰ)[J].Chaos, Solitons and Fractals,2005,23(2):469-475. doi: 10.1016/j.chaos.2004.04.027
    [5]
    LI Ji-bin,DAI Hui-hui.On the studies of sigular travelling wave equations[A].Dynamical System Approach[C].Beijing:Science Press, 2007.
    [6]
    Chow S N,Hale J K.Method of Bifurcation Theory[M].New York:Springer-Verlag,1981.
    [7]
    Guckenheimer J,Holmes P J.Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields[M].New York:Springer-Verlag, 1983.
    [8]
    Perko L.Differential Equations and Dynamical Systems[M].New York:Springer-Verlag,1991.
    [9]
    Li Y A,Olver P J.Convergence of solitary-wave solutionsin a perturbed bi-Hamiltonian dynamical system Ⅰ:Compactons and peakons[J].Discrete and Continuous Dynamical Systems,1997,3(3):419-432. doi: 10.3934/dcds.1997.3.419
    [10]
    Li Y A,Olver P J.Convergence of solitary-wave solutionsin a perturbed bi-Hamiltonian dynamical system Ⅱ: Complexanalytic behaviour and convergence to non-analytic solutions[J].Discrete and Continuous Dynamical Systems,1998,4(1):159-191.
    [11]
    LI Ji-bin,LIU Zhen-rong.Smooth and non-smooth travelling waves in a nonlinearly dispersive equation[J].Appl Math Modelling,2000,25(1):41-56. doi: 10.1016/S0307-904X(00)00031-7
    [12]
    LI Ji-bin,LIU Zhen-rong.Travelling wave solutions for a class of nonlinear dispersive equations[J].Chin Ann of Math,2002,23B(3):397-418.
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