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<p>In this paper, we prove the existence of explicit exact peakon, periodic peakon and solitary wave solutions of a two-dimensional nonlinear dispersive wave equation modeling finite deformations in a prestressed hyperelastic plate. By using the method of dynamical systems, under given parameter conditions, we obtain bifurcations of the phase portraits for the corresponding traveling wave dynamical system. Corresponding to different level curves, we derive possible exact explicit parametric representations of the periodic peakon, peakon, smooth periodic wave solution as well as solitary solutions.</p>

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Exact Peakon, Periodic Peakon and Solitary Wave Solutions of the General Chen Equation: Dynamical System Approach

  • 期刊论文

  • 发表日期：

    2026年1月28日

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  • Shimin Li,
  • Jibin Li

摘要

In this paper, we prove the existence of explicit exact peakon, periodic peakon and solitary wave solutions of a two-dimensional nonlinear dispersive wave equation modeling finite deformations in a prestressed hyperelastic plate. By using the method of dynamical systems, under given parameter conditions, we obtain bifurcations of the phase portraits for the corresponding traveling wave dynamical system. Corresponding to different level curves, we derive possible exact explicit parametric representations of the periodic peakon, peakon, smooth periodic wave solution as well as solitary solutions.