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## Soliton Turbulence in Approximate and Exact Models for Deep Water Waves

We investigate and compare soliton turbulence appearing as a result of modulational

instability of the homogeneous wave train in three nonlinear models for surface gravity waves:

the nonlinear Schrödinger equation, the super compact Zakharov equation, and the fully nonlinear

equations written in conformal variables. We show that even at a low level of energy and average

wave steepness, the wave dynamics in the nonlinear Schrödinger equation fundamentally differ from

the dynamics in more accurate models. We study energy losses of wind waves due to their breaking

for large values of total energy in the super compact Zakharov equation and in the exact equations

and show that in both models, the wave system loses 50% of energy very slowly, during few days.