Hydrodynamics dromion excitations in systems of self-propelled particles

This paper investigates the propagation of dromion-like waves in systems composed of self-propelled entities. Starting from the continuity and hydrodynamic equations governing particle dynamics, we derive a system of Davey–Stewartson type I equations with complex coefficients using the multi-scale expansion method. A modulational instability analysis reveals parameter regimes conducive to the emergence of localized wave structures, notably dromions. These regimes are intricately linked to physical effects such as inter-particle collisions, diffusive transport, and directional changes during particle motion. By applying a separation-of-variables approach to the derived equations, we construct dromion-type excitations comprising both short- and long-wave components. Numerical simulations of these components illustrate the system’s dynamical response to variations in key parameters, providing insight into the behavior of active matter under nonlinear wave modulation.