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Recently, the HADES experiment at GSI has provided preliminary data on thedirected flow, $v_1$ elliptic flow, $v_2$ and triangular flow, $v_3$ of protonsin Au+Au reactions at a beam energy of 1.23 A GeV. Here we present atheoretical discussion of these flow harmonics within the UrQMD transportapproach. We show that all flow harmonics, including the triangular flow,provide a consistent picture of the expansion of the system, if potentialinteractions are taken into account. Investigating the dependence of the flowharmonics on the nuclear interaction potentials it is shown that especially$v_3$ can serve as a sensitive probe for the nuclear equation of state at suchlow energies. The triangular flow and its excitation function with respect tothe reaction-plane were calculated for the first time and indicate a complexinterplay of the time-evolution of the system and the initial conditions at lowbeam-energies. Our study also indicates a significant softening of the equationof state at beam energies above $E_{\mathrm{lab}}> 7$A GeV which can beexplored by at the future FAIR facility.

Directed, elliptic and triangular flow of protons in Au+Au reactions at 1.23 AGeV: A theoretical analysis of the recent HADES data