Rogue waves emerging from the resonant interaction of three waves

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We introduce a novel family of analytic solutions of the three-wave resonant interaction equations to the purpose of modeling unique events, i.e. "amplitude peaks" which are isolated in space and time. The description of these solutions is likely to be a crucial step in the understanding and forecasting of rogue-waves in a variety of multi-component wave dynamics, from oceanography to optics, from plasma physics to acoustics.