# Accession Number:

## AD0609067

# Title:

## ASYMPTOTIC THEORY OF WAVE-PROPAGATION.

# Descriptive Note:

## Research rept.,

# Corporate Author:

## NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES

# Personal Author(s):

# Report Date:

## 1964-10-01

# Pagination or Media Count:

## 103.0

# Abstract:

A general method is presented for finding asymptotic solutions of problems in wave-propagation. The method is applicable to linear symmetric-hyperbolic partial differential equations and to the integro-differential equations for the electromagnetic field in a dispersive medium. These equations may involve a large parameter lambda. In the electromagnetic case lambda is a characteristic frequency of the medium. The parameter may also appear in initial data or in the source terms of the equations, in a variety of different ways. This gives rise to a variety of different types of asymptotic solutions. The expansion procedure is a ray method, i.e., all the functions that appear in the expansion satisfy ordinary differential equations along certain space-time curves called rays. In general, these rays do not lie on characteristic surfaces, but may, for example, fill out the interior of a characteristic hypercone. They are associated with an appropriately defined group velocity. In subsequent papers the ray method developed here will be applied to acoustic wave propagation, Cerenkov radiation, transition radiation, and other phenomena of wave-propagation. Author

# Descriptors:

- (*WAVE PROPAGATION
- DIFFERENTIAL EQUATIONS)
- (*ELECTROMAGNETIC FIELDS
- EQUATIONS)
- (*INTEGRAL EQUATIONS
- WAVE PROPAGATION)
- (*DIFFERENTIAL EQUATIONS
- WAVE PROPAGATION)
- PARTIAL DIFFERENTIAL EQUATIONS
- ELECTROMAGNETIC RADIATION
- OPERATORS (MATHEMATICS)
- MATRICES(MATHEMATICS)
- FIELD THEORY
- FOURIER ANALYSIS
- VECTOR ANALYSIS
- SERIES(MATHEMATICS)
- THEORY
- ACOUSTICS
- SCATTERING
- PROPAGATION
- OSCILLATION
- HAMILTONIAN
- COMPLEX VARIABLES
- CERENKOV RADIATION
- TRANSFORMATIONS (MATHEMATICS)