HU Jian-lan, ZHANG Han-lin. Analytical Solutions for Some Nonlinear Evolution Equations[J]. Applied Mathematics and Mechanics, 2003, 24(5): 545-550.
Citation: HU Jian-lan, ZHANG Han-lin. Analytical Solutions for Some Nonlinear Evolution Equations[J]. Applied Mathematics and Mechanics, 2003, 24(5): 545-550.

Analytical Solutions for Some Nonlinear Evolution Equations

  • Received Date: 2001-11-01
  • Rev Recd Date: 2002-11-05
  • Publish Date: 2003-05-15
  • The following partial differential equations are studied:generalized fifth-order KdV equation,water wave equation,kupershmidt equation,couples KdV equation.The analytical solutions to these problems via using various ansatzes by introducing a second-order ordinary differential equation are found out.
  • loading
  • [1]
    LI Zheng-yuan. The existence of travelling front solutions for reaction-diffusion system[J]. J Partial Differential Equations,1992,5(1):17-22.
    Ablowitz M J, Zepetella A. Explicit solutions of Fisher's equation for a special wave speed[J]. Bull Math Bial,1979,41(4):835-840.
    Abdlkaser M A. Travelling wave solutions for a generalized Fisher equation[J]. J Math Anal Appl,1982,85(2):287.
    Wilson G. The affine lie algebra C2(1) and an equation of Hirota and Satsuma[J].Phys Lett A,1982,89(7):332.
    Hirota R, Satsuam J.Soliton solutions of a coupled Korteweg-de Vries equation[J].Phys Lett A,1981,85(8-9):407.
    Olive P L. Hamiltonian and non-hamiltonian models for water waves[A].In: Lecture Notes in Physics[M].No 195,New York: Springer-verlag,1984,273-290.
    Fuchssteiner B, Oevel W,Wiwianka W. Computer-algebra methods for investigation of hereditary operators of high order soliton equations[J]. Comput Physics Comm,1987,44(1):47-55.
    Murray J D. Mathematical Biology[M].New York: Springer, 1989.
    LU Bao-quan, et al. Solitary wave solutions of some systems of coupled nonlinear equations[J]. Phys Lett A,1993,180(1-2):61.
    WANG Ming-xin,XIONG Shu-lin,YE Qi-xiao,et al. Explicit wave front solutions of Noyes-field systems for the Belousov-Zhabotinskii reaction[J]. J Math Anal Appl,1994,182(3):705.
    WANG Ming-xin.Nonlinear Equations of Parabolic Type[M].Beijing: Science Press,1994.
    FENG Xue-shang. Exact wave front solutions to two generalized coupled nonlinear physical equations[J]. Phys Lett A, 1996,213(3-4):167.
    WANG Ming-liang,ZHOU Yu-bin,LI Zhi-bin,et al. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics[J]. Phys Lett A,1996,216(1-5):67.
    FAN En-gui,ZHANG Hong-qiang. New exact solutions to a system of coupled KdV equations[J]. Phys Lett A, 1998,245(5):389.
    FAN En-gui,ZHANG Hong-qiang.A note on the homogenerous balance method[J]. Phys Lett A,1998,246(5):403.
    LU Hong-jun, WANG Ming-xin. Exact soliton solutions of some nonlinear physical models[J]. Phys Lett A,1999,255(4-6):249.
  • 加载中


    通讯作者: 陈斌,
    • 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 (2208) PDF downloads(923) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint