Non-degenerate multi-rogue waves and easy ways of their excitation

TL;DR

This paper demonstrates that multi-component systems can easily generate multiple rogue waves from simple initial conditions, expanding the known family of rogue wave solutions and explaining their occurrence in various physical contexts.

Contribution

It introduces a broader class of non-degenerate rogue waves in multi-component systems and shows they can be excited with simple initial conditions unlike single-component cases.

Findings

Multiple rogue waves can be excited simultaneously with simple initial conditions.

Expanded the family of Peregrine-type solutions to include non-degenerate rogue waves.

Results applicable to oceanography, Bose-Einstein condensates, plasmas, and optical fibers.

Abstract

In multi-component systems, several rogue waves can be simultaneously excited using simple initial conditions in the form of a plane wave with a small amplitude single-peak perturbation. This is in drastic contrast with the case of multi-rogue waves of a single nonlinear Schr\"{o}dinger equation (or other evolution equations) that require highly specific initial conditions to be used. This possibility arises due to the higher variety of rogue waves in multi-components systems each with individual eigenvalue of the inverse scattering technique. In theory, we expand the limited class of Peregrine-type solutions to a much larger family of non-degenerate rogue waves. The results of our work may explain the increased chances of appearance of rogue waves in crossing sea states (wind generated ocean gravity waves that form nonparallel wave systems along the water surface) as well as provide new possibilities of rogue wave observation in a wide range of multi-component physical systems such as multi-component Bose-Einstein condensates, multi-component plasmas and in birefringent optical fibres.