The Numerical Inverse Scattering Transform: Nonlinear Fourier Analysis and Nonlinear Filtering of Oceanic Surface Waves

Download or read book The Numerical Inverse Scattering Transform: Nonlinear Fourier Analysis and Nonlinear Filtering of Oceanic Surface Waves written by A. R. Osborne and published by . This book was released on 1993 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Fourier analysis is discussed as it arises from the exact spectral solution to large classes of nonlinear wave equations which are integrable by the inverse scattering transform (IST). The approach may be viewed as a generalization of the ordinary, linear Fourier transform or Fourier series. Numerical methods are discussed which allow for implementation of the approach as a tool for the time series analysis of oceanic wave data. I specifically consider the case for shallow water, where integrable nonlinear wave motion is governed by the Korteweg-de Vries equation with periodic/quasi-periodic boundary conditions. Numerical procedures given herein allow the computation of a nonlinear Fourier series for a measured time series. The nonlinear oscillation modes of KdV obey a linear superposition law, just as do the sine waves of a linear Fourier series. However, the KdV basis functions themselves are highly nonlinear, undergo nonlinear interactions with each other and are distinctly non sinusoidal. I analyze surface wave data from the Adriatic Sea and apply the concept of nonlinear filtering to enhance understanding of nonlinear interactions.