Weakly Nonlinear High Frequency Waves.

Abstract

In this paper we derive a method for finding small amplitude high frequency solutions to hyperbolic systems of quasilinear partial differential equations. Our solution is the sum of two parts: (i) a superposition of small amplitude high frequency waves; (ii) a slowly varying 'mean solution'. Each high frequency wave displays nonlinear distortion of the wave profile and shocks may form. Shock conditions are derived for conservative systems. Different high frequency waves do not interact provided the frequencies and wave numbers of two waves are not linearly related to those of a third. The mean solution is found by solving a linear partial differential equation. This method generalizes Whitham's nonlinearization technique 9 for single waves, to problems where many waves are present. We obtain these results by generalizing a scheme first proposed by Choquet-Bruhat 1 which employs the method of multiple scales. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1982
Accession Number
ADA116246

Entities

People

  • John Hunter

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Acoustic Propagation
  • Acoustics
  • Asymptotic Series
  • Computational Science
  • Differential Equations
  • Electrical Solitons
  • Equations
  • Formulas (Mathematics)
  • Frequency
  • Gas Dynamics
  • Mathematics
  • Method Of Characteristics
  • Partial Differential Equations
  • Sound Waves
  • Ultrasounds
  • United States
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Combustion Dynamics and Shock Wave Physics.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Plasma Physics / Magnetohydrodynamics