Vector rogue waves on a double-plane wave background

TL;DR

This paper derives and analyzes vector rogue wave solutions on a double-plane wave background, revealing complex superpositions and profiles, and providing explicit conditions for different rogue wave patterns.

Contribution

It introduces a method to derive rogue wave solutions on a double-plane wave background and explores their superpositions and profiles, expanding understanding of rogue wave dynamics.

Findings

Rogue waves can be excited from resonant perturbations on double-plane backgrounds.

Vector rogue waves can be decomposed into two separate rogue waves.

Explicit phase diagrams for rogue wave pattern superpositions are provided.

Abstract

We study rogue wave excitation dynamics on a double-plane wave background through deriving rogue wave solution on the background. The results indicate that rogue wave still can be excited successfully from resonant perturbations with the two plane wave backgrounds. The obtained vector rogue wave can be decomposed to two rogue waves located on the two backgrounds separately. This enables us to investigate the superpositions of two of the three well-known fundamental rogue wave patterns, mainly including eye-shaped, anti-eye-shaped, and four-petaled one. The explicit conditions for different possible superpositions are clarified by a phase diagram for rogue wave pattern on each plane wave background. The detail analysis indicate that the rogue wave admits many different profiles, in contrast to the ones reported before. The studies can be extended directly to investigate other localized waves on double-plane wave background and even more plane waves involved cases.