Accession Number : ADA116246

Title :   Weakly Nonlinear High Frequency Waves.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Hunter,John

PDF Url : ADA116246

Report Date : May 1982

Pagination or Media Count : 60

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)

Descriptors :   *Partial differential equations, *Linear differential equations, *Waves, *High frequency, Hyperbolas, Mean, Shock, Profiles, Methodology, Amplitude

Subject Categories : Theoretical Mathematics
      Radiofrequency Wave Propagation

Distribution Statement : APPROVED FOR PUBLIC RELEASE