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We discuss the formation of large amplitude waves for sea states characterized by JONSWAP spectra with random phases. In this context we discuss experimental results performed in one of the largest wave tank facilities in the world. We present experimental evidence that the tail of the cumulative probability function of the wave heights for random waves strongly depends on the ratio between the wave steepness and the spectral bandwidth. When this ratio, called the Benjamin-Feir Index, is large the Rayleigh distribution clearly underestimates the occurrence of large amplitude waves. Our experimental results are also successfully compared with previously performed numerical simulations of the Dysthe equation.
We study numerically the nonlinear stage of modulational instability (MI) of cnoidal waves, in the framework of the focusing one-dimensional Nonlinear Schrodinger (NLS) equation. Cnoidal waves are the exact periodic solutions of the NLS equation and
Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the statistics of the
We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation. Using a mul
A generalized plasma model having warm ions, iso-thermal electrons, super-thermal electrons and positrons is considered to theoretically investigate the modulational instability (MI) of ion-acoustic waves (IAWs). A standard nonlinear Schr{o}dinger eq
The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly unstable un