Accession Number : AD0716530

Title :   Theory of Nonlinear Waves.

Descriptive Note : Scientific rept.,

Corporate Author : INNSBRUCK UNIV (AUSTRIA) INST FOR THEORETICAL PHYSICS

Personal Author(s) : Schmid,Joachim M.

Report Date : 15 OCT 1970

Pagination or Media Count : 39

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)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, WAVE PROPAGATION), (*NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), DISPERSION RELATIONS, INTEGRALS, APPROXIMATION(MATHEMATICS), POWER SERIES, WAVE FUNCTIONS, AUSTRIA

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE