Solitons, cnoidal waves and nonlinear Interactions in shallow-water ocean surface waves

We analyze shallow-watersurfacewave data from the Adriatic Sea using a nonlinear generalization of Fourier analysis based upon the periodic inverse scattering transform in the θ-function representation for the Korteweg-de Vries (KdV) equation. While linear Fourier analysis superposes sine waves, the nonlinear Fourier approach superposes cnoidalwaves (the travelling wave solution to KdV) plus their mutual, nonlinearinteractions. A new procedure is presented for the nonlinear low-pass and band-pass filtering of measured wave trains. We apply the approach to a measured time series and discuss the dynamics of solitons and the physics of the nonlinearinteractions in terms of global, spatio-temporal phase shifts amongst the cnoidalwave