We consider a system of two cubic-quintic nonlinear Schrödinger equations in two dimensions, coupled by repulsive cubic terms. We analyze situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and analyze their interaction. We find a realization of D'Alembert's paradox for small velocities and nontrivial drag forces for larger ones. We present numerical analysis including the search of static and traveling form-preserving solutions along with simulations of the dynamical evolution in some representative examples.
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