This report considers a set of interacting self-propelled particles immersed in a viscous and noisy environment. The explored particle interaction does not distinguish between alignments and anti-alignments of the self-propulsion forces. More specifically, we considered a set of self-propelled apolar aligning attractive particles. Consequently, there is no genuine flocking transition because the system has no global velocity polarization. Instead, another self-organized motion emerges, where the system forms two counter-propagating flocks. This tendency leads to the formation of two counter-propagating clusters for short-range interaction. Depending on the parameters, these clusters interact, exhibiting two of the four classical behaviors of counter-propagating dissipative solitons (which does not imply that a single cluster must be recognized as a soliton). They interpenetrate and continue their movement after colliding or forming a bound state where the clusters remain together. This phenomenon is analyzed using two mean-field strategies: an all-to-all interaction that predicts the formation of the two counter-propagating flocks and a noiseless approximation for cluster-to-cluster interaction, which explains the solitonic-like behaviors. Furthermore, the last approach shows that the bound states are metastables. Both approaches agree with direct numerical simulations of the active-particle ensemble.
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