  We investigate the effect of self-interactions on the shape and oscillations
of the solitonic core profile of condensed fuzzy dark matter systems without
the backdrop of a halo, revealing universal features in terms of an
appropriately scaled interaction strength characterizing the crossover between
the weakly- and strongly-interacting regimes. Our semi-analytical results are
further confirmed by spherically symmetric simulations of the
Gross-Pitaevskii-Poisson equations. Inverting our obtained relations, we
highlight a degeneracy that could significantly affect constraints on the boson
mass in the presence of repulsive boson self-interactions and propose the
simultaneous extraction of static and dynamical solitonic features as a way to
uniquely constrain both the boson mass and self-interactions.
