From modulational instability to focusing dam breaks in water waves
Félicien Bonnefoy, Alexey Tikan, François Copie, Pierre Suret, Guillaume Ducrozet, Gaurav Prabhudesai, Guillaume Michel, Annette Cazaubiel, Eric Falcon, Gennady El, Stéphane Randoux
Abstract
The Benjamin-Feir, or modulational, instability has been regarded as the main mechanism of spontaneous disintegration of broad weakly nonlinear wavepackets in deep water waves. We report water wave experiments with another result. For a range of initial parameters, a nearly rectangular initial wavepacket develops a strongly nonlinear modulation with two dispersive shock waves expanding from the edges of the wavepacket towards the center at finite speed. This is supported by theory based on the semiclassical limit of the one-dimensional focusing nonlinear Schrodinger equation.