Rogue Waves in (2+1)-Dimensional Three-Wave Resonant Interactions

TL;DR

This paper investigates the formation and dynamics of rogue waves in a (2+1)-dimensional three-wave resonant interaction system, revealing novel line-shaped and pattern-rich rogue wave solutions from various backgrounds.

Contribution

It derives and illustrates new rogue wave solutions from constant, lump-soliton, and dark-soliton backgrounds, highlighting their unique shapes and interactions.

Findings

Fundamental rogue waves are line-shaped from constant backgrounds.

Multi-rogue waves show multiple intersecting lines.

Dark-soliton background rogue waves feature novel half-line and lump shapes.

Abstract

Rogue waves in (2+1)-dimensional three-wave resonant interactions are studied. General rogue waves arising from a constant background, from a lump-soliton background and from a dark-soliton background have been derived, and their dynamics illustrated. For rogue waves arising from a constant background, fundamental rogue waves are line-shaped, and multi-rogue waves exhibit multiple intersecting lines. Higher-order rogue waves could also be line-shaped, but they exhibit multiple parallel lines. For rogue waves arising from a lump-soliton background, they could exhibit distinctive patterns due to their interaction with the lump soliton. For rogue waves arising from a dark-soliton background, their intensity pattern could feature half-line shapes or lump shapes, which are very novel.