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

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.

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1993
Accession Number
ADP008733

Entities

People

  • A. R. Osborne

Organizations

  • University of HawaiĘ»i System

Tags

DTIC Thesaurus Topics

  • Adriatic Sea
  • Electrical Solitons
  • Equations
  • Filtration
  • Fourier Analysis
  • Fourier Series
  • Inverse Scattering
  • Oceanography
  • Physical Oceanography
  • Scattering
  • Shallow Water
  • Sine Waves
  • Surface Waves
  • Time Series Analysis
  • Wave Equations
  • Waves

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Wave Propagation and Nonlinear Chaotic Dynamics.