  We investigate the Zeno dynamics of the optical rogue waves. Considering
their usage in modeling rogue wave dynamics, we analyze the Zeno dynamics of
the Akhmediev breathers, Peregrine and Akhmediev-Peregrine soliton solutions of
the nonlinear Schrodinger equation. We show that frequent measurements of the
wave inhibits its movement in the observation domain for each of these
solutions. We analyze the spectra of the rogue waves under Zeno dynamics. We
also analyze the effect of observation frequency on the rogue wave profile and
on the probability of lingering of the wave in the observation domain. Our
results can find potential applications in optics including nonlinear
phenomena.
