Interactions and Focusing of Nonlinear Water Waves

The coupled cubic nonlinear Schr\"odinger (CNLS) equations are used to study modulational instabilities of a pair of nonlinearly interacting two-dimensional waves in deep water. It has been shown that the full dynamics of these interacting waves gives rise to localized large-amplitude wavepackets (wave focusing). In this short letter we attempt to verify this result numerically using a Fourier spectral method for the CNLS equations.