In this paper, the dimensionless $n$-component Hirota (alias the $n$-Hirota) equation is investigated, which describes the wave propagations of $n$ ultrashort optical fields in a fiber. Starting from the modified Darboux transform and its Lax pair with initial non-zero plane-wave conditions, we find the novel multi-parametric families of rational vector rogue wave (RW) solutions for the $n$-Hirota equation. Furthermore, some weak and strong interactions of rational vector RWs are exhibited for the $n$-Hirota equation with $n=2,3,4,5,6$ in detail. In particular, we also deduce the rational vector $W$-shaped dark and bright solitons of the $n$-component complex mKdV equation, whose representative wave structures are illustrated for $n=2,3,4,5$. Finally, the effect of a small non-integrable deformation of the 3-Hirota equation is explored numerically on the excitation of vector RWs in terms of the Fourier spectral method. These obtained rational vector RW and W-shaped soliton solutions will be useful to further explore the related nonlinear wave phenomena in the sense of multi-component physical systems with non-zero backgrounds.

在本文中，无量纲 $n$-component Hirota（别名 $n$-Hirota) 方程进行了研究，该方程描述了波的传播 $n$光纤中的超短光场。从改进的 Darboux 变换及其具有初始非零平面波条件的 Lax 对开始，我们找到了新的有理向量流氓波 (RW) 解的多参数族，用于$n$-广田方程。此外，有理向量 RW 的一些弱相互作用和强相互作用对于$n$-Hirota 方程与 $n=2,3,4,5,6$详细。特别地，我们还推导出有理向量$宽$形状的暗和亮孤子 $n$-分量复数 mKdV 方程，其代表性的波结构图示为 $n=2,3,4,5$. 最后，根据傅立叶谱方法，数值地探讨了 3-Hirota 方程的小不可积变形对矢量 RW 激发的影响。这些获得的有理向量 RW 和 W 形孤子解将有助于进一步探索具有非零背景的多分量物理系统意义上的相关非线性波现象。