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Peaked singular wave solutions associated with singular curves

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  • Bi, Qinsheng

Abstract

We present new types of singular wave solutions with peaks in this paper. When a heteroclinic orbit connecting two saddle points intersects with the singular curve on the topological phase plane for a generalized KdV equation, it may be divided into segments. Different combinations of these segments may lead to different singular wave solutions, while at the intersection points, peaks on the waves can be observed. It is shown for the first time that there coexist different types of singular waves corresponding to one heteroclinic orbit.

Suggested Citation

  • Bi, Qinsheng, 2007. "Peaked singular wave solutions associated with singular curves," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 417-423.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:2:p:417-423
    DOI: 10.1016/j.chaos.2005.09.074
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    References listed on IDEAS

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    1. 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.
    2. Zhang, Zhengdi & Bi, Qinsheng & Wen, Jianping, 2005. "Bifurcations of traveling wave solutions for two coupled variant Boussinesq equations in shallow water waves," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 631-643.
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