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PARAMETER REGION FOR EXISTENCE OF SOLITONS IN GENERALIZED KdV EQUATION

PARAMETER REGION FOR EXISTENCE OF SOLITONS IN GENERALIZED KdV EQUATION
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摘要 This paper considers the generalized KdV equation with or without natural boundary conditions and provides a parameter region for solitons and solitary waves, and also modifies a result of Zabuskys. The solitary bifurcation has been discussed. This paper considers the generalized KdV equation with or without natural boundary conditions and provides a parameter region for solitons and solitary waves, and also modifies a result of Zabuskys. The solitary bifurcation has been discussed.
作者 Sheng PingxingDept. of Math., College of Natural Science, Shanghai Univ., Shanghai 200436,China.
出处 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2003年第2期173-178,共6页 高校应用数学学报（英文版）（B辑）
基金 Research partially supported by Shanghai Development Grant of Education Committee(# 2 0 0 0 A1 0 )
关键词 generalized KdV equation traveling waves SOLITON homoclinic (heteroclinic) orbit bifurcation. generalized KdV equation, traveling waves, soliton, homoclinic (heteroclinic) orbit, bifurcation.
分类号 O175 [理学—基础数学]
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参考文献11

  • 1Novikov, S. , et al. , Theory of Solitons--the inverse scattering method, New York:Consultants Bureau, 1984.
  • 2Drazin, P. G. , Solitons, London Mathematical Society Lecture Note Series (85), Cambridge:Cambridge Univ. Press, 1983.
  • 3Gardner, C. S. , et al, Method for solving the KdV equation, Phys. Rev. Letter, 1967, 19: 1095-1097.
  • 4Gu Chaohao, Hu Hesheng, The unified explicit form of B cklund transformations for generalized hierarchies of the KdV equation, Lett. Math. Phys. , 1986,11: 325-335.
  • 5Gu Chaohao, Soliton Theory and Its Applications, Hangzhou: Zhejiang Scientific Press, 1990 (in Chinese ).
  • 6Hirota, R. , Exact Solution of the KdV equation for multiple collisions of soliton, Phys. Rev. Lett.1971,27 : 1192-1194.
  • 7Wahlquist,H. D. , Estabrook, F. B. , B cklund transformation for soliton of the KdV equation,Phys. Rev. Lett., 1973,31:1386-1390.
  • 8Liu Shida, Liu Shikuo, Solitary Wave and Turbulence, Shanghai. Shanghai Scientific and Technological Education Publishing House, 1994(in Chinese).
  • 9Zabusky, N. J. , A synergetic approach to problems of nonlinear dispersive wave propagation and interaction, In: W.F. Ames, ed. , Nonlinear Partial Differential Equations, New York: Academic Press, 1967,223-258.
  • 10Sheng Pingxing, Strange attractor of KdV-Burgers equation, Journal of Shanghai Univ. , 1997,1(2) :91-94.
Applied Mathematics(A Journal of Chinese Universities)
2003年 第2期

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