  We study the Majorana modes, both equilibrium and Floquet, which can appear
at the edges of the Kitaev model on the honeycomb lattice. We first present the
analytical solutions known for the equilibrium Majorana edge modes for both
zigzag and armchair edges of a semi-infinite Kitaev model and chart the
parameter regimes of the model in which they appear. We then examine how edge
modes can be generated if the Kitaev coupling on the bonds perpendicular to the
edge is varied periodically in time as periodic $\delta$-function kicks. We
derive a general condition for the appearance and disappearance of the Floquet
edge modes as a function of the drive frequency for a generic $d$-dimensional
integrable system. We confirm this general condition for the Kitaev model with
a finite width by mapping it to a one-dimensional model. Our numerical and
analytical study of this problem shows that Floquet Majorana modes can appear
on some edges in the kicked system even when the corresponding equilibrium
Hamiltonian has no Majorana mode solutions on those edges. We support our
analytical studies by numerics for finite sized system which show that periodic
kicks can generate modes at the edges and the corners of the lattice.
