Theory of Nonlinear Waves.

Abstract

The paper is a review of papers which handle nonlinear waves with an averaging technic developed by Whitham. If it is possible to derive the differential equations governing the problem from a variational principle the Lagrangian can be averaged over one period. From the averaged Lagrangian averaged conservation equations are derived and from these one finds a second order differential equation in terms of frequency, wavenumber and amplitude - that is a dispersion equation. Besides the frequency dispersion an amplitude dispersion occurs too. The distortion of the waveform depends on whether the Dispersion equation is elliptic or hyperbolic. The nonlinearity may produce phase jumps and discontinuities of the wavenumber. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 15, 1970
Accession Number
AD0716530

Entities

People

  • Joachim M. Schmid

Organizations

  • University of Innsbruck

Tags

DTIC Thesaurus Topics

  • Amplitude
  • Differential Equations
  • Dispersions
  • Electrical Solitons
  • Equations
  • Frequency
  • Frequency Shift
  • Variational Principles
  • Waves

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)