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Bifurcations of traveling wave solutions in a compound KdV-type equation

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  • Zhang, Zhengdi
  • Bi, Qinsheng

Abstract

By using the theory of planar dynamical systems to a compound KdV-type nonlinear wave equation, the bifurcation boundaries of the system are obtained in this paper. These bifurcation sets divide the parameter space into different regions, which correspond to qualitatively different phase portraits and therefore different types of the solutions may exist in different regions. The parameter conditions for the existence of solitary wave solutions and uncountably infinite, many smooth and non-smooth, periodic wave solutions are therefore obtained.

Suggested Citation

  • Zhang, Zhengdi & Bi, Qinsheng, 2005. "Bifurcations of traveling wave solutions in a compound KdV-type equation," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1185-1194.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:4:p:1185-1194
    DOI: 10.1016/j.chaos.2004.06.013
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    Cited by:

    1. Bi, Qinsheng, 2007. "Peaked singular wave solutions associated with singular curves," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 417-423.
    2. Wazwaz, Abdul-Majid, 2006. "Two reliable methods for solving variants of the KdV equation with compact and noncompact structures," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 454-462.
    3. Ge, Zheng-Ming & Zhang, An-Ray, 2007. "Chaos in a modified van der Pol system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1791-1822.

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