  We find the existence of sub-Planck scale structures in the P{\"o}schl-Teller
potential, which is an exactly solvable potential with both symmetric and
asymmetric features. We analyze these structures in both cases by looking at
the Wigner distribution of the state evolved from an initial coherent state up
to various fractional revival times. We also investigate the sensitivity to
perturbations of the P{\"o}schl-Teller potential and we verify that, similar to
the harmonic oscillator, the presence of sub-Planck structure in phase space is
responsible for a high sensitivity to phase-space displacements.
