# The interaction of Airy waves and solitons in the three-wave system

## TL;DR

This paper investigates the interactions between Airy waves and solitons within a three-wave system involving quadratic nonlinearity, revealing stable wave behaviors, transformation processes during collisions, and conditions for quasi-elastic interactions.

## Contribution

It introduces the study of Airy wave and soliton collisions in a three-wave $ ext{chi}^{(2)}$ system, highlighting stability and transformation phenomena not observed in other nonlinear systems.

## Key findings

- Single-wave Airy waves are stable and unaffected by nonlinearity.
- Collisions can transform Airy waves into solitons or form bound states.
- High-velocity collisions tend to be quasi-elastic.

## Abstract

We employ the generic three-wave system, with the $\chi ^{(2)}$ interaction between two components of the fundamental-frequency (FF) wave and second-harmonic (SH) one, to consider collisions of truncated Airy waves (TAWs) and three-wave solitons in a setting which is not available in other nonlinear systems. The advantage is that the single-wave TAWs, carried by either one of the FF component, are not distorted by the nonlinearity and are stable, three-wave solitons being stable too in the same system. The collision between mutually symmetric TAWs, carried by the different FF components, transforms them into a set of solitons, the number of which decreases with the increase of the total power. The TAW absorbs an incident small-power soliton, and a high-power soliton absorbs the TAW. Between these limits, the collision with an incident soliton converts the TAW into two solitons, with a remnant of the TAW attached to one of them, or leads to formation of a complex TAW-soliton bound state. At large velocities, the collisions become quasi-elastic.