The Peregrine soliton is a solution of the one-dimensional nonlinear Schrödinger equation that can be written in normalized units as follows :
with  the spatial coordinate and  the temporal coordinate.  being the envelope of a surface wave in deep water. The dispersion is anomalous and the nonlinearity is self-focusing (note that similar results could be obtained for a normally dispersive medium combined with a defocusing nonlinearity).
The Peregrine analytical expression is:
so that the temporal and spatial maxima are obtained for  and .