# Freezing Optical Rogue Waves by Zeno Dynamics

## TL;DR

This paper explores how frequent measurements can inhibit the movement of optical rogue waves modeled by solutions of the nonlinear Schrödinger equation, with potential applications in nonlinear optics.

## Contribution

It demonstrates the application of Zeno dynamics to optical rogue waves, analyzing their spectra and profiles under frequent observation, a novel approach in optical wave control.

## Key findings

- Frequent measurements inhibit rogue wave movement.
- Observation frequency affects rogue wave profiles.
- Spectral properties are altered under Zeno dynamics.

## Abstract

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.