In this paper, we qualitatively study the effect of the Coriolis force on traveling waves of the rotation-two-component Camassa–Holm system in the rotating fluid, which is a model in the equatorial water waves, from the perspective of dynamical systems. We obtain the explicit critical rotational speed $\mathrm{\Omega }=\frac{1}{2(A+c)}$ (A is a parameter of the system characterizing a linear underlying shear flow and c is the wave speed), which reflects the Coriolis force. Based on this critical vorticity, we obtain phase portraits of the system under exact explicit parameters conditions. Then we not only show the existence of various bounded traveling waves including smooth solitary waves, peakons and kink waves, under corresponding exact explicit parameters conditions, but also obtain their exact expressions. Of particular interest is that we find that kink waves (which were not found previouly) exist only when $\mathrm{\Omega }>\frac{1}{2(A+c)}$, that is, the rotational speed Ω should be greater than $\frac{1}{2(A+c)}$.

在本文中，我们从动力系统的角度定性研究了科里奥利力对旋转流体中旋转双分量Camassa-Holm系统行波的影响，该旋转流体是赤道水波中的模型。我们得到明确的临界转速$\mathrm{欧姆}=\frac{\mathrm{1个}}{\mathrm{2个}(A+C)}$（A是表征线性底层剪切流的系统参数，c是波速），它反映了科里奥利力。基于这个临界涡度，我们在精确的显式参数条件下获得了系统的相图。然后我们不仅证明了各种有界行波包括光滑孤立波、峰子和扭结波在相应的精确显式参数条件下的存在性，而且得到了它们的精确表达式。特别有趣的是，我们发现扭结波（以前没有发现）仅在$\mathrm{欧姆}>\frac{\mathrm{1个}}{\mathrm{2个}(A+C)}$，即转速Ω应大于$\frac{\mathrm{1个}}{\mathrm{2个}(A+C)}$.