  We show that one-dimensional Floquet trimer arrays with periodically
oscillating waveguides support two different and co-existing types of
topological Floquet edge states in two different topological gaps in Floquet
spectrum. In these systems nontrivial topology is introduced by longitudinal
periodic oscillations of the waveguide centers, leading to the formation of
Floquet edge states in certain range of oscillation amplitudes despite the fact
that the structure spends half of the period in ``instantaneously''
nontopological phase, and only during other half-period it is
``instantaneously'' topological. Two co-existing Floquet edge states are
characterized by different phase relations between bright spots in the unit
cell -- in one mode these spots are in-phase, while in other mode they are
out-of-phase. We show that in focusing nonlinear medium topological Floquet
edge solitons, representing exactly periodic nonlinear localized Floquet
states, can bifurcate from both these types of linear edge states. Both types
of Floquet edge solitons can be stable and can be created dynamically using
two-site excitations.
