Vector rogue waves on a double-plane wave background

Abstract

We study the dynamics of rogue waves on a double-plane wave background in two-component coupled systems. The results indicate that many different patterns can still be evolved from resonant perturbations with the two plane waves background. The obtained vector rational solutions can be decomposed into two rational solutions located on the two plane waves separately. This enables us to investigate the superposition of several 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. The analysis indicates that the obtained rational solution described patterns admit many different profiles, in contrast to the ones reported before. The studies can be extended to investigate other localized waves on double-plane wave backgrounds and even more plane waves involved cases in multi-component coupled systems.