  We present a nonlinear multimode superconducting electroacoustic system,
where the interplay between superconducting kinetic inductance and
piezoelectric strong coupling establishes an effective Kerr nonlinearity among
multiple acoustic modes at 10 GHz that could hardly be achieved via intrinsic
mechanical nonlinearity. By exciting this multimode Kerr system with a single
microwave tone, we further demonstrate a coherent electroacoustic frequency
comb and provide theoretical understanding of multimode nonlinear interaction
in the superstrong coupling limit. This nonlinear superconducting
electroacoustic system sheds light on the active control of multimode resonator
systems and offers an enabling platform for the dynamic study of microcombs at
microwave frequencies.
