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非线性耗散-色散方程行波解的存在性

M·B·A·曼索

M·B·A·曼索. 非线性耗散-色散方程行波解的存在性[J]. 应用数学和力学, 2009, 30(4): 479-483.
引用本文: M·B·A·曼索. 非线性耗散-色散方程行波解的存在性[J]. 应用数学和力学, 2009, 30(4): 479-483.
M. B. A. Mansour. Existence of Traveling Wave Solutions for a Nonlinear Dissipative-Dispersive Equation[J]. Applied Mathematics and Mechanics, 2009, 30(4): 479-483.
Citation: M. B. A. Mansour. Existence of Traveling Wave Solutions for a Nonlinear Dissipative-Dispersive Equation[J]. Applied Mathematics and Mechanics, 2009, 30(4): 479-483.

非线性耗散-色散方程行波解的存在性

详细信息
    作者简介:

    M·B·A·曼索,M.B.A.Mtansour(E-mail:mah_nansour@hotmail.com).

  • 中图分类号: O175.29;O347;O193

Existence of Traveling Wave Solutions for a Nonlinear Dissipative-Dispersive Equation

  • 摘要: 非线性耗散-色散方程出现在很多物理现象中.基于动力系统理论,利用几何奇摄动法,当耗散项系数充分小时,研究了该方程行波解的存在性.结果表明,在常微分方程组的一个三维系统中,行波依靠二维的慢流变形而存在.然后利用Melnikov方法,在该流形中建立了同宿轨道的存在性,它与方程的孤立波解相对应.进一步,给出了某些数值计算,得到该波轨道的近似.
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    [2] Lou S Y, Huang G X, Ruan H Y. Exact solitary waves in a convecting fluid[J].J Phys A,1991,24(11): L587-L590.
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    [7] Ruan S G, Xiao D M. Stability of steady states and existence of travelling waves in a vector-disease model[J].Proc Roy Soc Edinburgh, Sect A,2004,134(5): 991-1011. doi: 10.1017/S0308210500003590
    [8] Ktrychko Y N, Bartuccelli M V, Blyuss K B. Persistence of traveling wave solutions of a fourth order diffusion system[J].J Comput Appl Math,2005,176(2): 433-443. doi: 10.1016/j.cam.2004.07.028
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出版历程
  • 收稿日期:  2008-06-09
  • 修回日期:  2009-03-06
  • 刊出日期:  2009-04-15

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