Accession Number : AD0619956

Title :   ASYMPTOTIC SOLUTION OF A DISPERSIVE HYPERBOLIC EQUATION WITH VARIABLE COEFFICIENTS.

Descriptive Note : Research rept.,

Corporate Author : NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES

Personal Author(s) : Bleistein,Norman ; Lewis,Robert M.

Report Date : JUN 1965

Pagination or Media Count : 80

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)

Descriptors :   (*BOUNDARY VALUE PROBLEMS, SERIES(MATHEMATICS)), (*SERIES(MATHEMATICS), PARTIAL DIFFERENTIAL EQUATIONS), FIELD THEORY, WAVE PROPAGATION, DIFFRACTION, PROPAGATION, FREQUENCY

Distribution Statement : APPROVED FOR PUBLIC RELEASE