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    • Dynamics and Bifurcations of Travelling Wave Solutions of $R(m, n)$ Equations

      Dahe Feng Jibin Li

      Volume 117 Issue 4 November 2007 pp 555-574

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/117/04/0555-0574

    • Keywords

       

      $R(m, n)$ equations; solitary wave; periodic wave; breaking wave; solitary cusp wave; periodic cusp wave.

    • Abstract

       

      By using the bifurcation theory and methods of planar dynamical systems to $R(m, n)$ equations, the dynamical behavior of different physical structures like smooth and non-smooth solitary wave, kink wave, smooth and non-smooth periodic wave, and breaking wave is obtained. The qualitative change in the physical structures of these waves is shown to depend on the systemic parameters. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above waves are given. Moreover, some explicit exact parametric representations of travelling wave solutions are listed.

    • Author Affiliations

       

      Dahe Feng1 Jibin Li2

      1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, People’s Republic of China
      2. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, People’s Republic of China

    • Dates

       
      Published
      November 2007
      Manuscript received
      17 September 2006
      Manuscript revised
      14 January 2007

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