
Accession Number : ADA116246
Title : Weakly Nonlinear High Frequency Waves.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIVMADISON 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 ChoquetBruhat 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