In this work, the $S$- and $P$-wave $bar{D}^ast K^ast$ interactions are studied in a coupled-channel formalism to understand the recently observed $X_0(2900)$ and $X_1(2900)$ at LHCb. The experimental event distributions can be well described, and two states with $I(J^P)=0(0^+)$ and $0(1^-)$ are yielded in an unified framework with the same set of parameters. Their masses and widths are determined to be $[m,Gamma]_{0^+}=[2873.2^{+10.8}_{-12.2},72.2^{+9.6}_{-8.3}]$ MeV and $[m,Gamma]_{1^-}=[2905.6^{+14.6}_{-10.7},52.5_{-1.3}^{+9.5}]$ MeV from the pole analyses, respectively. The masses of the $0^+$ and $1^-$ states are consistent with the experimental data, but the width of the $0^+$ state is larger than that of the $1^-$ one. The $X_1(2900)$ can be interpreted as the $P$-wave excitation of the ground-state $X_0(2900)$ in the hadronic molecular picture. The $S$- and $P$-wave multiplets in the $bar{D}^ast K^ast$ system have many members, so the present peak in the $D^-K^+$ invariant mass distributions might contain multi subpeaks. In order to probe the fine structures behind the single whole peak now, more refined measurements in the $B^+to D^+D^-K^+$ decay channel are necessary.
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