Stability of weakly nonlinear deep-water waves in two and three dimensions

Abstract
The stability of a weakly nonlinear wave train on deep water to two- and three-dimensional modulations is investigated using an improved approximation due to Zakharov (1968). The results are expressible in simple analytical forms, and show good quantitative agreement with available experimental data and exact numerical calculations over a broad range of wave steepness in the unidirectional case.