Abstract
Asymptotically exact nonlocal fourth-order nonlinear evolution equations are derived for two counterpropagating capillary-gravity wave packets on the surface of water of infinite depth. On the basis of these equations a stability analysis is made for a uniform standing capillary-gravity wave for longitudinal perturbation. The instability conditions and an expression for the maximum growth rate of instability are obtained. Significant deviations are noticed between the results obtained from third-order and fourth-order nonlinear evolution equations.
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