We observe the dispersive breaking of cosine long waves [Phys. Rev. Lett. 15, 240 (1965)] in shallow water, characterising the highly nonlinear "multi-soliton" fission over variable conditions. We provide new insight into the interpretation of the results by analysing the data in terms of the periodic inverse scattering transform for the Korteweg-de Vries equation. In a wide range of dispersion and nonlinearity, the data compare favourably with our analytical estimate, based on a rigorous WKB approach, of the number of emerging solitons. We are also able to observe experimentally the universal Fermi-Pasta-Ulam recurrence in the regime of moderately weak dispersion.

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The problem of existence of stable nonlinear groups of gravity waves in deep water is revised by means of laboratory and numerical simulations with the focus on intense waves.

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.

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