  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.
