A modified nonlinear Schrodinger equation for broader bandwidth gravity waves on deep water

The modified nonlinear Schrodinger equation of Dysthe [Proc. Roy. Sec. Lend. Ser. A, 369, 105-114 (1979)] is extended by relaxing the narrow bandwidth constraint to make it more suitable for application to a realistic ocean wave spectrum. The new equation limits the bandwidth of unstable wave number perturbations of a Stokes wave in good agreement with the exact results of McLean et al. [Phys. Rev. Lett. 46, 817-820 (1981)]. Results are presented for the parametric bifurcation boundary between collinear and oblique most unstable side band perturbations of a Stokes wave.