Harihar Khanal, Stefan Mancas, Shahrdad Sajjadi
A theoretical and computational study is undertaken for the 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). The coupled cubic nonlinear Schr\"odinger (CNLS) equations are used to derive a nonlinear dispersion equation which give rise to new class of modulational instabilities and demonstrates the dependence of obliqueness of the interacting waves. The computations, due to nonlinear wave-wave interactions, waves that are separately modulationally stable can give rise to the formation of large-amplitude coherent wave packets with amplitudes several times that of the initial waves. In the case for the original Benjamin-Feir instability, in contrast, waves disintegrate into a wide spectrum.
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http://arxiv.org/abs/1301.4219
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