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.
Firstly, in section 4 1 we use weakly-nonlinear theory to analytically derive the stability of long-wave perturbations to small-amplitude solutions
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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.