Accession Number : ADA195970

Title :   Mathematical Problems of Nonlinear Wave Propagation and of Waves in Heterogeneous Media.

Descriptive Note : Final rept. 1 Oct 86-30 Sep 87,

Corporate Author : STANFORD UNIV CA APPLIED MATHEMATICS GROUP

Personal Author(s) : Keller, Joseph B

PDF Url : ADA195970

Report Date : 31 Mar 1988

Pagination or Media Count : 9

Abstract : The asymptotic behavior of weakly nonlinear waves at caustics is determined for nonlinear wave propagation. A theory is developed for the propagation of short waves of any strength. A method is found for analyzing the stability of a large class of nonlinear waves. The theory of acoustoelasticity is reduced by considering nonlinear effects on waves in granular material. The theory of waves in heterogeneous media analyzed scattering by slender bodies. The pass and stop bands are determined for waves in stratified periodic media. The same is done for an acoustic medium containing rigid spheres arranged in a simple cubic lattice. The amplitude equations are determine for resonantly-interacting water waves in water of nonuniform depth. Keywords: Nonlinear waves; Heterogenous media; Reciprocal theorems; Effective parameters; Pouring flows; Surface flow; Weir flow; Caustics of nonlinear waves; Asymptotic behavior of stability regions for Hill's equation; Stability of periodic plane waves; Lower bounds of permeability; Newtons second law; Stability of plane wave solutions of nonlinear systems; Resonantly interacting water waves; Nonlinear hyperbolic waves. (jhd)

Descriptors :   *CAUSTICS, *ACOUSTIC WAVES, *UNDERWATER ACOUSTICS, ACOUSTICS, AMPLITUDE, ASYMPTOTIC SERIES, DEPTH, EQUATIONS, FLOW, GRANULES, HETEROGENEITY, HIGH FREQUENCY, HYPERBOLAS, INTERACTIONS, MATHEMATICS, MEDIA, NONLINEAR ALGEBRAIC EQUATIONS, NONLINEAR PROPAGATION ANALYSIS, NONLINEAR SYSTEMS, NONUNIFORM, PERMEABILITY, PLANE WAVES, REGIONS, RIGIDITY, SCATTERING, SIMPLE CUBIC LATTICES, SLENDER BODIES, SOLUTIONS(GENERAL), SPHERES, STABILITY, STRATIFICATION, SURFACES, THEOREMS, THEORY, WATER, WATER WAVES, WAVE PROPAGATION, WAVES

Subject Categories : Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE