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

We analyze shallow-water surface wave data from the Adriatic Sea using a no nlinear generalization of Fourier analysis based upon the periodic inverse scattering transform in the theta-function representation for the Korteweg- de Vries (KdV) equation. While linear Fourier analysis superposes sine wave s, the nonlinear Fourier approach superposes cnoidal waves (the travelling wave solution to KdV) plus their mutual, nonlinear interactions. A new proc edure is presented for the nonlinear low-pass and band-pass filtering of me asured wave trains. We apply the approach to a measured time series and dis cuss the dynamics of solitons and the physics of the nonlinear interactions in terms of global, spatio-temporal phase shifts amongst the cnoidal waves . Copyright (C) 1998 Elsevier Science B.V.