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Stationary-phase asymptotic of a Klein-Gordon wave along a subluminal ray

For zero initial velocity and Fourier amplitude

a (k)

, observation along

x = V t

with

0 \leq V < c

selects the two stationary wavenumbers

\pm k_{0}

, where

k_{0} = \frac{A V}{c ^{2} - V ^{2}} .

Writing

s = c^{2} - V^{2}

, the leading oscillation has angular frequency

A s

and amplitude proportional to

t^{- 1/2}

.

Table of contents 62 1
- Upward zero crossings of an oscillatory stationary-phase tail Stationary-phase asymptotic of a Klein-Gordon wave along a subluminal ray 21

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