Rigorous Bloch-Floquet analysis of the Euler equations confirms the Benjamin-Feir instability via figure-eight eigenvalue splitting and yields exact stability regions for gravity-capillary Stokes waves.
The disintegration of wave trains on deep water. Part 1. Theory
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Surface tension stabilizes the modulational instability of large-amplitude gravity-capillary waves at smaller values than weakly nonlinear theory predicts, with nonmonotonic dependence on tension.
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On the stability of large-amplitude gravity-capillary surface waves
Surface tension stabilizes the modulational instability of large-amplitude gravity-capillary waves at smaller values than weakly nonlinear theory predicts, with nonmonotonic dependence on tension.