Anisotropic flows in heavy-ion collisions provide a basic experimental observable to understand nuclear collision dynamics and to constrain the dense nuclear matter equation of state (EOS). Within the framework of the lattice Boltzmann-Uehling-Uhlenbeck transport model, we present a systematic study of proton anisotropic flow observables measured by the HADES Collaboration, by utilizing the recently developed nuclear effective interaction based on the density-, momentum-, and isospin-dependent N5LO Skyrme pseudopotential. In particular, we investigate the impacts of the momentum dependence of nucleon mean-field potentials, the stiffness of the symmetric nuclear matter (SNM) EOS, the high-density behaviors of the symmetry energy, and the in-medium modification of nucleon-nucleon elastic cross sections on proton directed ($v_1$), elliptic ($v_2$), triangular ($v_3$), and quadrangular ($v_4$) flows in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=2.4\text{GeV}$. Our results show that the proton anisotropic flows are strongly sensitive to the momentum dependence of the nucleon mean-field potential as well as the incompressibility coefficient $K_0$ of SNM. In addition, the transverse momentum dependence of the proton $v_2$ exhibits a modest sensitivity to the higher-order skewness coefficient $J_0$ and kurtosis coefficient $I_0$ of SNM as well as the momentum dependence of the symmetry potential, while the transverse momentum dependence of the proton $v_1$ is shown to modestly depend on the in-medium modification of nucleon-nucleon elastic cross sections. Moreover, the high-density symmetry energy seems to have limited effects on the proton anisotropic flows. These findings highlight the necessity of considering the momentum dependence of nucleon mean-field potentials including the symmetry potential, the higher-order characteristic parameters of the SNM EOS beyond $K_0$, and the in-medium modification of nucleon-nucleon elastic cross sections, in future Bayesian transport model analyses on proton anisotropic flows in heavy-ion collisions at HADES energies, for the purpose of extracting information on the nuclear matter EOS as well as the associated underlying nuclear effective interactions.

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• Collective flow
• Equations of state of nuclear matter
• Low & intermediate energy heavy-ion reactions
• Nucleon-nucleon interactions