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<p>In this paper, the generalized Fornberg–Whitham equation with parabolic law nonlinearity is studied by the bifurcation method of differential equations and the method of phase portraits analysis. Six bifurcation curves are obtained and the (<i>c</i>,&#xa0;<i>k</i>)-plane is divided into 45 parts. Equivalently, more different types of traveling wave solution and more diverse dynamic properties are obtained for the generalized Fornberg–Whitham equation. In some parametric conditions, a large number of new traveling wave solutions are obtained by symbolic calculation, including periodic wave solution, solitary wave, periodic pseudo-peakon and compacton solution. In particular, periodic pseudo-peakon is globally smooth and compacton solution is defined in a bounded open interval.</p>

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Traveling Wave Solutions and Bifurcations for Generalized Fornberg–Whitham Equation with Parabolic Law Nonlinearity

  • 期刊论文

  • 发表日期：

    2025年3月28日

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  • Deniu Yang

摘要

In this paper, the generalized Fornberg–Whitham equation with parabolic law nonlinearity is studied by the bifurcation method of differential equations and the method of phase portraits analysis. Six bifurcation curves are obtained and the (c, k)-plane is divided into 45 parts. Equivalently, more different types of traveling wave solution and more diverse dynamic properties are obtained for the generalized Fornberg–Whitham equation. In some parametric conditions, a large number of new traveling wave solutions are obtained by symbolic calculation, including periodic wave solution, solitary wave, periodic pseudo-peakon and compacton solution. In particular, periodic pseudo-peakon is globally smooth and compacton solution is defined in a bounded open interval.