Fig. 2
Controlling the extreme wave genus. a Numerical simulation of the control of the final state after a propagation distance \(L=2.5\) mm for an initial beam waist \({W}_{0}=140\,\upmu\)m (\({I}_{0}=\frac{P}{{U}_{0}{W}_{0}}=0.38\times 1{0}^{5}\) W/m2). Axis \(x\) represents the beam transverse direction, axis \(t\) the time of output detection. b Initial beam intensity: a super-Gaussian wave centered at \(x=150\,\upmu\)m of height \({I}_{0}\) and width \({W}_{0}\). c, d Focusing dispersive shock waves occurrence: c represents the beam intensity at \(t=5\) s, when the wave breaking has just occurred, so two lateral intense wave trains regularize the box discontinuity and start to travel towards the beam central part; d the beam intensity at \(t=11\) s, which exhibits the two counterpropagating DSWs reaching the center \(x=150\,\upmu\)m. e–g Akhmediev breathers and Peregrine solitons generation: beam intensity at e \(t=49\) s, f \(t=98\) s, and g \(t=120\) s, after the two dispersive shock waves superposition and the formation of Akhmediev breathers with period increasing with \(t\). Since a Peregrine soliton is an Akhmediev breather with an infinite period, increasing \(t\) is tantamount to generating central intensity peaks, locally described by Peregrine solitons
