Soliton basis states in shallow-water ocean surface waves

The inverse scattering transform for the periodic Korteweg--de Vries equation is used to analyze surface-wave data obtained in the Adriatic Sea and a robust solition spectrum is found. While the solitons are not observable in the data due to the presence of energetic radiation modes, a new nonlinear filtering technique renders the solitons visible. Numerical simulations support the existence of solitons in the measurements and suggest that, as a wave train propagates into shallow water, the solitons grow at the expense of the radiation.