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

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

OSBORNE, Alfred Richard;SERIO, Marina;BERGAMASCO, Laura Maria;
1998-01-01

Abstract

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
1998
123
64
81
http://dx.doi.org/10.1016/S0167-2789(98)00112-2
Inverse scattering transform; Numerical methods; Nonlinear Fourier analysis; Nonlinear basis functions; Ocean waves; Theta functions; Hyperelliptic functions
Osborne A.R.; Serio M.; Bergamasco L.; Cavaleri L.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/110384
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