One-dimensional wave dispersion in layered media

Author: 

Farmer, C
Ockendon, J
Ockendon, H
Allwright, D

Publication Date: 

1 January 2015

Journal: 

SIAM Journal on Applied Mathematics

Last Updated: 

2020-01-22T21:16:39.957+00:00

Issue: 

5

Volume: 

75

DOI: 

10.1137/15M101138X

page: 

2128–2146-

abstract: 

Homogenisation theory reveals that long one-dimensional waves propagating in a medium with spatially periodic wave speed can behave like dispersive waves in an appropriately homogenised medium. However the precise time and length scales over which this dispersive behaviour is a good approximation are not clear. This paper describes what happens in a specific case when the sound speed and initial conditions allow the problem to be reduced to a finite system of difference equations which can be solved exactly. The long-time asymptotics are compared with the predictions of homogenisation theory and new light is shed on the dispersion phenomenon

Symplectic id: 

538176

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article