  Realizing Majorana modes (MMs) in condensed-matter systems is of vast
experimental and theoretical interests, and some signatures of MMs have been
measured already. To facilitate future experimental observations and to explore
further applications of MMs, generating many MMs at ease in an experimentally
accessible manner has become one important issue. This task is achieved here in
a one-dimensional $p$-wave superconductor system with the nearest- and
next-nearest-neighbor interactions. In particular, a periodic modulation of
some system parameters can induce an effective long-range interaction (as
suggested by the Baker-Campbell-Hausdorff formula) and may recover
time-reversal symmetry already broken in undriven cases. By exploiting these
two independent mechanisms at once we have established a general method in
generating many Floquet MMs via periodic driving.
