From rogue waves to solitons

TL;DR

This paper explores how rogue waves can transform into solitons under the influence of higher-order effects like dispersion, self-steepening, and Raman shifts, revealing mechanisms for wave evolution in nonlinear systems.

Contribution

It systematically demonstrates the transformation mechanisms of rogue waves into solitons using a generalized nonlinear Schrödinger equation with higher-order effects.

Findings

Rogue waves can evolve into solitons under third-order dispersion and self-steepening.

Self-steepening can cause a finite rogue wave to become an infinite volume soliton.

Raman shifts lead to decelerating rogue waves that generate red-shifted radiation and become slow-moving solitons.

Abstract

Using a generalized nonlinear Schr\"odinger equation, we investigate the transformation of a fundamental rogue wave to a collection of solitons. Taking the third-order dispersion, self-steepening, and Raman-induced self-frequency shift as the generalizing effects, we systematically observe how a fundamental rogue wave has an impact on its surrounding continuous wave background and reshapes its own characteristics while a group of solitons are created. We show that under the influence of the self-steepening effect, a finite-volume rogue wave can transform into an infinite volume soliton. Also, we find that with the Raman-induced self-frequency shift, a decelerating rogue wave generates a red-shifted Raman radiation while the rogue wave itself turns into a slow-moving soliton. We show that each of these effects has an element of mechanism that favors the rogue wave to generate a group of solitons while the rogue wave itself also becomes one of these solitons.