Darboux transformation and dark rogue wave states arising from two-wave resonance interaction

Exact rogue wave solutions of the long wave–short wave resonance equation are obtained via Darboux transformations. Compared to the real long-wave field which always features a single hump structure, the short-wave field can be manifested as bright rogue wave, intermediate rogue wave, or dark rogue wave, depending on the subtle nonlinearity driven by the long-wave field.