Fractional derivative method for describing solitons on the surface of deep water

The fractional derivative method is used to take wave dispersion into account in the wave equation when describing the propagation of gravitational soliton waves on the surface of deep water. This approach is similar to that used to obtain the Korteweg–de Vries equation for solitons on the surface of shallow water, where the dispersion term in the wave equation is the third derivative of the velocity. It provides an alternative to the well-known approach of Zakharov and others based on the model of the nonlinear Schrödinger equation. The obtained nonlinear integral equation can be solved numerically.