Recurrent solutions of Alber's equation for random water-wave fields

The study addresses the linear instability of narrow spectra homogeneous seas and its subsequent evolution in time, subject to inhomogeneous disturbances. Specifically, we study unidirectional spectra, where according to the kinetic equation no spectral evolution is expected. In the region of instability, recurrent evolution is discovered. This recurrence is the stochastic counterpart of the Fermi–Pasta–Ulam recurrence obtained for the cubic Schrödinger equation.