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A higher order nonlinear evolution equation for much broader bandwidth gravity waves in deep water

Debsarma S., Das K. P.

International Journal of Applied Mechanics and Engineering

2007

Vol. 12, no 2

557-563

A higher order nonlinear evolution equation for gravity waves in deep water is derived from Zakharov's integral equation which is valid for a much broader bandwidth gravity waves than considered previously. The instability regions in the perturbed wave-number space for a uniform Stokes wave obtained from this equation is shown to fit nicely those obtained by McLean et al. [Phys. Rev. Lett. 46, 817-820(1981)] by exact numerical method.