  Nonlinear superlattices exhibit unique features allowing for wave
manipulations. Despite the increasing attention received, the underlying
physical mechanisms and the evolution process of the band structures and
bandgaps in strongly nonlinear superlattices remain unclear. Here we establish
and examine strongly nonlinear superlattice models (three triatomic models) to
show the evolution process of typical nonlinear band structures based on
analytical and numerical approaches. We find that the strongly nonlinear
superlattices present particular band degeneration and bifurcation, accompanied
with the vibration mode transfer in their unit cells. The evolution processes
and the physical mechanisms of the band degeneration in different models are
clarified with the consideration of the mode transfer. The observed
degeneration may occur as the shifting, bifurcating, shortening, merging or
disappearing of dispersion curves, all depending on the arrangement of the
coupled nonlinear elements. Meanwhile, the dimension of the unit cell reduces,
alongside changes in the frequency range and mechanisms (Bragg and local
resonance) of the bandgaps. These findings answer some foundamental questions
peritinent to the study of nonlinear periodic structures, nonlinear crystals
and nonlinear metamaterials, which are of interest to the broad community of
physics
