A key challenge in investigating the dynamics of mobile impurities immersed in field excitations is the need to include the entanglement between the impurities and the ambient excitations. To meet this challenge, we need to assume that the effective mass of impurities is finite rather than infinite. Here we theoretically investigate how finite-mass impurities interact with nonlinear excitations (i.e., solitons) in polaritonic Bose-Einstein condensates (BECs), which are inherently non-equilibrium. We analytically derive the interaction phase diagram between bright solitons and impurities in polariton BECs using the Lagrange variational method and the Gross-Pitaevsky equation for divergence. We show that solitons can be transmitted, trapped, or reflected when they collide with impurities. Our work goes beyond previous work in the context of equilibrium systems and opens new perspectives for understanding the non-equilibrium dynamics of mobile impurities immersed in non-Liar field excitations.

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