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We study experimentally, in a large-scale basin, the propagation ofunidirectional deep water gravity waves stochastically modulated in phase. Weobserve the emergence of nonlinear localized structures that evolve on astochastic wave background. Such a coexistence is expected by the integrableturbulence theory for the nonlinear Schr{\"o}dinger equation (NLSE), and wereport the first experimental observation in the context of hydrodynamic waves.We characterize the formation, the properties and the dynamics of thesenonlinear coherent structures (solitons and extreme events) within theincoherent wave background. The extreme events result from the strongsteepening of wave train fronts, and their emergence occurs after roughly onenonlinear length scale of propagation (estimated from NLSE). Solitons arisewhen nonlinearity and dispersion are weak, and of the same order of magnitudeas expected from NLSE. We characterize the statistical properties of thisstate. The number of solitons and extreme events is found to increase all alongthe propagation, the wave-field distribution has a heavy tail, and the surfaceelevation spectrum is found to scale as a frequency power-law with an exponent--4.5 $\pm$ 0.5. Most of these observations are compatible with the integrableturbulence theory for NLSE although some deviations (e.g. power-law spectrum,asymmetrical extreme events) result from effects proper to hydrodynamic waves.

Coexistence of solitons and extreme events in deep water surface waves