Accession Number : ADP008733

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

Corporate Author : HAWAII UNIV HONOLULU DEPT OF OCEANOGRAPHY

Personal Author(s) : Osborne, A. R.

Report Date : NOV 1993

Pagination or Media Count : 23

Abstract : 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.

Descriptors :   *NONLINEAR DIFFERENTIAL EQUATIONS, *FOURIER ANALYSIS, *WAVE EQUATIONS, OCEAN SURFACE, SPATIAL FILTERING, TIME SERIES ANALYSIS, ADRIATIC SEA.

Subject Categories : Theoretical Mathematics
      Physical and Dynamic Oceanography

Distribution Statement : APPROVED FOR PUBLIC RELEASE