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    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/088/01/0017

    • Keywords

       

      Modified generalized Vakhnenko equation; cusped solitons; loop solitons; periodic cusp wave solutions; smooth periodic wave solutions; pseudopeakon solitons; smooth soliton solutions.

    • Abstract

       

      By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.

    • Author Affiliations

       

      JUNJUN XIAO1 DAHE FENG 1 2 XIA MENG1 YUANQUAN CHENG1

      1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, People’s Republic of China
      2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou 550025, People’s Republic of China

    • Dates

       
      Published
      16 January 2017
      Manuscript received
      12 May 2015
      Manuscript revised
      24 May 2016
      Accepted
      17 June 2016
      Early published
      13 December 2016

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