Hongler, Max-Olivier2022-01-062022-01-062022-01-062021-12-2910.3390/fractalfract6010015https://infoscience.epfl.ch/handle/20.500.14299/184328In this paper, a dissipative version of the Benjamin–Ono dynamics is shown to faithfully model the collective evolution of swarms of scalar Cauchy stochastic agents obeying a follow-the-leader interaction rule. Due to the Hilbert transform, the swarm dynamic is described by nonlinear and non-local dynamics that can be solved exactly. From the mutual interactions emerges a fat-tail soliton that can be obtained in a closed analytic form. The soliton median evolves nonlinearly with time. This behaviour can be clearly understood from the interaction of mutual agents.Benjamin–Ono dynamicsmaster equationsjump Markov processesinteracting Cauchy processesswarm dynamicsfat-tail soliton wavestext::journal::journal article::research article