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The bifurcation and peakon for K(2,2) equation with osmosis dispersion

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  • Xu, Chuanhai
  • Tian, Lixin

Abstract

In this paper, the qualitative analysis methods of a dynamical system are used to investigate the peaked wave solutions of K(2,2) equation with osmosis dispersion. The phase portrait bifurcation of the traveling wave system corresponding to the equation is given. The explicit expressions of the peaked solitary wave solution and the periodic cusp wave solution are obtained by using the portraits. The graph of the solution is given with the numerical simulation.

Suggested Citation

  • Xu, Chuanhai & Tian, Lixin, 2009. "The bifurcation and peakon for K(2,2) equation with osmosis dispersion," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 893-901.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:893-901
    DOI: 10.1016/j.chaos.2007.08.042
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    References listed on IDEAS

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    1. Yu, Liqin & Tian, Lixin & Wang, Xuedi, 2006. "The bifurcation and peakon for Degasperis–Procesi equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 956-966.
    2. Ismail, M.S. & Taha, T.R., 1998. "A numerical study of compactons," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(6), pages 519-530.
    3. Wazwaz, A.M., 2002. "General compactons solutions and solitary patterns solutions for modified nonlinear dispersive equations mK(n,n) in higher dimensional spaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(6), pages 519-531.
    4. Guo, Boling & Liu, Zhengrong, 2005. "Periodic cusp wave solutions and single-solitons for the b-equation," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1451-1463.
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