# Akhmediev Breathers and Peregrine Solitary Waves in a Quadratic Medium

## TL;DR

This paper demonstrates the existence of Akhmediev breathers and Peregrine waves in quadratic media, revealing new mechanisms for rogue wave formation and modulation instability in nonlinear optics.

## Contribution

It is the first to identify quadratic Akhmediev breathers and Peregrine waves in dispersive quadratic media, expanding understanding of localized structures in nonlinear optics.

## Key findings

- Existence of quadratic Akhmediev breathers
- Presence of Peregrine solitary waves in quadratic media
- Implications for rogue wave excitation in optics

## Abstract

We investigate the formation of optical localized nonlinear structures, evolving upon a non-zero background plane wave, in a dispersive quadratic medium. We show the existence of quadratic Akhmediev breathers and Peregrine solitary waves, in the regime of cascading second-harmonic generation. This finding opens a novel path for the excitation of extreme rogue waves and for the description of modulation instability in quadratic nonlinear optics.