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

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)

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Document Details

Document Type
Technical Report
Publication Date
Mar 31, 1988
Accession Number
ADA195970

Entities

People

  • Joseph B. Keller

Organizations

  • Stanford University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Bodies
  • Crystal Lattices
  • Crystal Structure
  • Cubic Lattices
  • Differential Equations
  • Electrical Solitons
  • Equations
  • Fluids
  • Granular Materials
  • Materials
  • Nonuniform
  • Partial Differential Equations
  • Plane Waves
  • Slender Bodies
  • Water Waves
  • Wave Propagation
  • Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Wave Propagation and Nonlinear Chaotic Dynamics.