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Bifurcation of solitons, peakons, and periodic cusp waves for \(\varvec{\theta }\)-equation

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Abstract

In this paper, we study the bifurcation of traveling wave solutions for \(\theta \)-equation using the bifurcation method and qualitative theory of dynamical systems. Not only smooth solitons but also explicit peakons and periodic cusp waves are obtained. In addition, we show that a new kind of phase portrait may admit peakons and infinitely many periodic cusp waves, in contrast to the traditional phase portraits. To the best of our knowledge, until now, this phenomenon has not appeared in any other literature. Some results of the previous studies are extended for this study.

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Acknowledgments

This research is supported by the foundation of Huaqiao University (No. 12BS223) and the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (No. ZQN-PY119).

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  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, People’s Republic of China

    Zhenshu Wen

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  1. Zhenshu Wen
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Wen, Z. Bifurcation of solitons, peakons, and periodic cusp waves for \(\varvec{\theta }\)-equation. Nonlinear Dyn 77, 247–253 (2014). https://doi.org/10.1007/s11071-014-1289-1

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  • DOI: https://doi.org/10.1007/s11071-014-1289-1

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