Title: Propagation of self-localised Q-ball solitons in the $^3$He universe,
Abstract: In relativistic quantum field theories, compact objects of interacting bosons
can become stable owing to conservation of an additive quantum number $Q$.
Discovering such $Q$-balls propagating in the Universe would confirm
supersymmetric extensions of the standard model and may shed light on the
mysteries of dark matter, but no unambiguous experimental evidence exists. We
report observation of a propagating long-lived $Q$-ball in superfluid $^3$He,
where the role of $Q$-ball is played by a Bose-Einstein condensate of magnon
quasiparticles. We achieve accurate representation of the $Q$-ball Hamiltonian
using the influence of the number of magnons, corresponding to the charge $Q$,
on the orbital structure of the superfluid $^3$He order parameter. This
realisation supports multiple coexisting $Q$-balls which in future allows
studies of $Q$-ball dynamics, interactions, and collisions.