Analysis of laboratory surface wave data using the scattering transform for the periodic Korteweg-de vries

We present a new approach which allows the analysis of nonlinear wave data within the framework of the periodic Korteweg-de Vries (KdV) equation. The method is based upon the periodic inverse scattering transform (IST) for KdV, a nonlinear generalization of linear Fourier series, in which the signal is decomposed into a linear superposition of nonlinearly interacting hyperelliptic functions. The KdV is assessed as a model equation in a large number of physical problems, including 1 + 1-dimensional nonlinear hydrodynamic wave propagation. We employ here IST to analyse laboratory surface wave data. Some physical implications are discussed; in particular we emphasize how the IST spectrum provides a much simpler interpretation of the wave motion than the linear Fourier transform, preserving the nonlinear mode amplitudes during the propagation of the waves.