FU Zun-tao, LIU Shi-da, LIU Shi-kuo, ZHAO Qiang. New Exact Solutions to KdV Equations With Variable Coefficients or Forcing[J]. Applied Mathematics and Mechanics, 2004, 25(1): 67-73.
Citation: FU Zun-tao, LIU Shi-da, LIU Shi-kuo, ZHAO Qiang. New Exact Solutions to KdV Equations With Variable Coefficients or Forcing[J]. Applied Mathematics and Mechanics, 2004, 25(1): 67-73.

New Exact Solutions to KdV Equations With Variable Coefficients or Forcing

  • Received Date: 2002-08-28
  • Rev Recd Date: 2003-07-31
  • Publish Date: 2004-01-15
  • Jacobi elliptic function expansion method is extended to construct the exact solutions to another kind of KdV equations,which have variable coefficients or forcing terms.And new periodic solutions obtained by this method can be reduced to the soliton-typed solutions under the limited condition.
  • loading
  • [1]
    Grimshaw R H J.Slowly varying solitary waves[J].Proc Roy Soc Lon A, 1979,368(1734):359—375. doi: 10.1098/rspa.1979.0135
    [2]
    Chan W L,ZHANG Xiao.Symmetries, conservation-laws and Hamiltonian structures of the nonisospectral and variable-coefficient KdV and mKdV equations[J].J Phys A,1995,28(2):407—419. doi: 10.1088/0305-4470/28/2/016
    [3]
    TIAN Chou.Symmetries and a hierarchy of the general KdV equation[J].J Phys A, 1987,20(2):359—366. doi: 10.1088/0305-4470/20/2/021
    [4]
    WANG Ming-liang.Solitary wave solutions for variant Boussinesq equations[J].Phys Lett A,1995,199(3/4):169—172. doi: 10.1016/0375-9601(95)00092-H
    [5]
    WANG Ming-liang.ZHOU Yu-bin,LI Zhi-bin. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics[J].Phys Lett A, 1996,216(1/5): 67—75. doi: 10.1016/0375-9601(96)00283-6
    [6]
    YANG Lei,ZHU Zheng-gang, WANG Ying-hai.Exact solutions of nonlinear equations[J].Phys Lett A, 1999,260(1/2):55—59. doi: 10.1016/S0375-9601(99)00482-X
    [7]
    YANG Lei,LIU Jiang,YANG Kong-qing.Exact solutions of nonlinear PDE, nonlinear transformations and reduction of nonlinear PDE to a quadrature[J].Phys Lett A, 2001,278(5): 267—270. doi: 10.1016/S0375-9601(00)00778-7
    [8]
    Parkes E J,Duffy B R.Travelling solitary wave solutions to a compound KdV-Burgers equation[J].Phys Lett A,1997,229(4):217—220. doi: 10.1016/S0375-9601(97)00193-X
    [9]
    FAN En-gui.Extended tanh-function method and its applications to nonlinear equations[J].Phys Lett A, 2000,277(45):212—218. doi: 10.1016/S0375-9601(00)00725-8
    [10]
    Hirota R.Exact N-solutions of the wave equation of long waves in shallow water and in nonlinear lattices[J].J Math Phys,1973,14(7):810—814. doi: 10.1063/1.1666400
    [11]
    Kudryashov N A.Exact solutions of the generalized Kuramoto-Sivashinsky equation[J].Phys Lett A, 1990,147(5/6):287—291. doi: 10.1016/0375-9601(90)90449-X
    [12]
    Otwinowski M,Paul R,Laidlaw W G.Exact travelling wave solutions of a class of nonlinear diffusion equations by reduction to a quadrature[J].Phys Lett A,1988,128(9):483—487. doi: 10.1016/0375-9601(88)90880-8
    [13]
    刘式适,付遵涛,刘式达,等.求某些非线性偏微分方程特解的一个简洁方法[J].应用数学和力学,2001,22(3):281—286.
    [14]
    YAN Chun-tao.A simple transformation for nonlinear waves[J].Phys Lett A,1996,224(1/2):77—84. doi: 10.1016/S0375-9601(96)00770-0
    [15]
    ZHANG Jie-fang,WU Feng-min.Simple soliton solution method for the (2+1)dimensional long disperive equation[J]. Chinese Physics,1999,8(5):326—331.
    [16]
    Porubov A V.Periodical solution to the nonlinear dissipative equation for surface waves in a convecting liquid layer[J].Phys Lett A,1996,221(6):391—394. doi: 10.1016/0375-9601(96)00598-1
    [17]
    Porubov A V,Velarde M G.Exact periodic solutions of the complex Ginzburg-Landau equation[J].J Math Phys,1999,40(2):884—896. doi: 10.1063/1.532692
    [18]
    Porubov A V,Parker D F. Some general periodic solutions to coupled nonlinear Schrdinger equations[J]. Wave Motion,1999,29(2):97—108. doi: 10.1016/S0165-2125(98)00033-X
    [19]
    LIU Shi-kuo,FU Zun-tao,LIU Shi-da,et al.Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations[J].Phys Lett A,2001,289(1/2):69—74. doi: 10.1016/S0375-9601(01)00580-1
    [20]
    Nirmala N,Vedan M J,Baby B V. Auto-Backland transformation, Lax pairs, Painleve property of a variable coefficient Korteweg-de Vries equation[J].J Math Phys, 1986,27(10):2640—2648. doi: 10.1063/1.527282
    [21]
    Oevel W H,Steeb W H.Painleve analysis for a time-dependent Kadomtsev-Petviashvili equation[J].Phys A,1984,103(2):239—242.
    [22]
    Steeb W H,Spicker B M.Kadomtsev-Petviashvili equation with explicit x and t dependence[J].Phys Rev A,1985,31(3):1952—1960. doi: 10.1103/PhysRevA.31.1952
    [23]
    ZHU Zuo-nong.Lax pairs,Backland transformation, solitary wave solution and infinite conservation laws of the general KP equation and MKP equation with variable coefficients[J]. Phys Lett A,1993,180(6):409—412. doi: 10.1016/0375-9601(93)90291-7
    [24]
    ZHU Zuo-nong. Painleve property, Backland transformation, Lax pairs and soliton-like solutions for a variable coefficient KP equation[J].Phys Lett A, 1993,182(2/3):277—281. doi: 10.1016/0375-9601(93)91071-C
    [25]
    Hong W,Jung Y D. Auto-Bckland transformation and analytic solutions for general variable-coefficent KdV equation[J].Phys Lett A,1999,257(3/4):149—152. doi: 10.1016/S0375-9601(99)00322-9
    [26]
    WANG Ming-liang,WAMG Yue-ming. A new Bckland transformation and multi-solitons to the KdV equations with general variable coefficients[J].Phys Lett A, 2001,287(3/4):211—216. doi: 10.1016/S0375-9601(01)00487-X
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2854) PDF downloads(686) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return