# Akhmediev breather signatures from dispersive propagation of a periodically phase-modulated continuous wave

## TL;DR

This paper explores the similarities between pulse localization in sinusoidally phase-modulated linear propagation and Akhmediev breather evolution in nonlinear systems, supported by numerical simulations and fiber optic experiments.

## Contribution

It demonstrates the qualitative similarities in pulse profiles between linear phase modulation and nonlinear Akhmediev breathers, providing new insights into their relationship.

## Key findings

- Profiles at maximum focusing are very similar in time and spectrum.
- Linear and nonlinear evolutions are similar near maximum focusing but diverge over longer distances.
- Experimental results in optical fibers confirm the numerical simulations.

## Abstract

We investigate in detail the qualitative similarities between the pulse localization characteristics observed using sinusoidal phase modulation during linear propagation and those seen during the evolution of Akhmediev breathers during propagation in a system governed by the nonlinear Schr{\"o}dinger equation. The profiles obtained at the point of maximum focusing indeed present very close temporal and spectral features. If the respective linear and nonlinear longitudinal evolutions of those profiles are similar in the vicinity of the point of maximum focusing, they may diverge significantly for longer propagation distance. Our analysis and numerical simulations are confirmed by experiments performed in optical fiber.

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Source: https://tomesphere.com/paper/1907.08426