Rogue waves in coupled Hirota systems

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Abstract
Exact rogue wave solutions of the coupled Hirota equations are obtained by using a Darboux dressing transformation. An analysis of the spectral parameter condition shows that our coupled rogue waves, equal or unequal in background height, always exist no matter what parameters have been chosen for the starting plane waves. We demonstrate that, compared with the decoupled ones, the coupled rogue waves can appear in a rather striking way, i.e., one wave exhibits a centrally humped structure, while the other may feature one single hole in the center\char22{}a dark rogue wave structure. It is expected that these unusual rogue wave structures due to the two-wave coupling may help explain the extreme wave events in deep ocean or other nonlinear dispersive media.

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