ASYMPTOTIC SOLUTION OF A DISPERSIVE HYPERBOLIC EQUATION WITH VARIABLE COEFFICIENTS.

Abstract

Initial-boundary value problems are considered for an energy conserving dispersive hyperbolic equation, the Klein-Gordon equation. This equation contains the main feature of dispersion: The speed of propagation depends on the frequency. The asymptotic expansion of solutions obtained by a technique which we call the ray method is compared with the asymptotic expansion of the exact solution. In every case considered, the solutions agree. Solutions are obtained for a series of initial-boundary value problems in one space dimension with variable coefficients. A new feature which is called space-time diffraction is found. This phenomenon has the following physical interpretation: A portion of the energy of a wave reaches a boundary surface and then gradually leaks off, leaving a diminishing residue on the boundary for all time. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1965
Accession Number
AD0619956

Entities

People

  • Norman Bleistein
  • Robert M. Lewis

Organizations

  • New York University

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Differential Equations
  • Diffraction
  • Dispersions
  • Equations
  • Frequency
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Materials Science and Engineering.

Technology Areas

  • Space