  Nonlinearities can have a profound influence on the dynamics and equilibrium
properties of discrete lattice systems. The simple case of two coupled modes
with self-nonlinearities gives rise to the rich bosonic Josephson effects. In
many-site arrays, nonlinearities yield a wealth of rich phenomena, including a
variety of solitonic excitations, the emergence of vortex lattices in the
presence of gauge fields, and the general support of chaotic dynamics. Here, we
experimentally explore a three-site mechanical ring with tunable gauge fields
and nonlinearities. We observe a macroscopic self-trapping transition that is
tunable by the magnetic flux, consistent with the equilibrium response. We
further observe novel behavior that appears only out of equilibrium, the
emergence of interaction-stabilized chiral solitary waves. These results
provide a starting point to explore nonlinear phenomena arising in larger
mechanical arrays coupled to static and dynamical gauge fields.
