Fig. 1

Topological classification of extreme waves. a Final states of the wave for a fixed initial waist \({W}_{0}=100\,\upmu\)m showing the generation of focusing dispersive shock waves (\(g=1\)), rogue waves (\(g \sim 2\)), and a soliton gas (\(g\ > > \ 2\)) after different time intervals in a photorefractive material (see text). b Phase diagram reporting the final states in terms of the parameter \(\epsilon\) and the initial beam waist. Transitions occur by fixing waist and varying \(\epsilon\) or, equivalently, the observation time \(t\). Different surfaces displayed in proximity of the various wave profiles, corresponding to the different regions in the phase diagram, outline the link between the topological classification of extreme waves in terms of the genus \(g\) and the topological classification of toroidal Riemann surfaces (for a sphere, \(g=0\), for a torus, \(g=1\), etc.)