Gray Soliton Formation in Ocean Waves Described by an Extended Nonlinear Schrödinger Equation with Pseudo-SRS

Gray soliton formation in ocean waves is examined using an extended nonlinear Schrödinger equation that incorporates wind-induced gain and a pseudo-stimulated Raman scattering term. A rigorous multiple scales expansion yields a third-order KdV-type evolution equation that accurately characterizes the leading-order dynamics in the weakly nonlinear regime. Extensive numerical simulations validate the analytical predictions.