  We report an experimental investigation of the effect of finite depth on the
statistical properties of wave turbulence at the surface of water in the
gravity-capillary range. We tune the wave dispersion and the level of
nonlinearity by modifying the depth of water and the forcing respectively. We
use space-time resolved profilometry to reconstruct the deformed surface of
water. When decreasing the water depth, we observe a drastic transition between
weak turbulence at the weakest forcing and a solitonic regime at stronger
forcing. We characterize the transition between both states by studying their
Fourier Spectra. We also study the efficiency of energy transfer in the weak
turbulence regime. We report a loss of efficiency of angular transfer as the
dispersion of the wave is reduced until the system bifurcates into the
solitonic regime.
