• The bifurcation and peakons for the special 𝐶(3, 2, 2) equation

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      https://www.ias.ac.in/article/fulltext/pram/083/03/0331-0340

    • Keywords

       

      $C(3, 2, 2)$ equation; peakons; bell-shaped solitary waves; periodic cusp waves.

    • Abstract

       

      In this paper, we investigate a special 𝐶(3, 2, 2) equation $$u_t + ku_x − u_{xxt} + 3(u^3)_x = u_x(u^2)_{xx} + u(u^2)_{xxx}$$.

      The bifurcation and some new exact representations of peakons, bell-shaped solitary wave solutions and periodic cusp wave solutions for the equation are obtained using the qualitative theory of dynamical systems. It is shown that the peakons are actually the limit of bell-shaped solitary waves and periodic cusp waves. Moreover, a new characteristic of non-smooth solutions, two peakons coexisting for the same wave speed, is found. Some previous results are extended.

    • Author Affiliations

       

      Lina Zhang1

      1. Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, People’s Republic of China
    • Dates

       
  • Pramana – Journal of Physics | News

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