The Zakharov integral equation for surface gravity waves is modified to include higher-order (quintet) interactions, for water of constant (finite or infinite) depth. This new equation is used to study some aspects of class I (4-wave) and class II (5-wave) instabilities of a Stokes wave.

Results of experiments on the evolution of the Peregrine breather (PB) in a wave tank are presented and compared with numerical simulations based on the Nonlinear Schrödinger (NLS) and the Dysthe equations. The experiments demonstrate notable deviation from the NLS solution due to significant asymmetric widening of the spectrum. Good agreement of measurements with the solutions of the Dysthe equation is obtained. Contrary to the PB NLS soliton, no return to the initial undisturbed wave train can be expected.