TITLE

Exact solutions for wave equations of two-layered media with smooth transition

AUTHOR(S)
Bluman, George; Kumei, Sukeyuki
PUB. DATE
January 1988
SOURCE
Journal of Mathematical Physics;Jan1988, Vol. 29 Issue 1, p86
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The wave equation c2(x)uxx-utt=0 is solved for wave speeds c(x) corresponding to two-layered media with smooth transition from layer to layer. The wave speed c(x) has four free parameters to fit a given medium. Solutions are constructed from invariant solutions of a related system of first-order partial differential equations that admit a four-parameter symmetry group. These solutions are superposed to solve general initial value problems for data with compact support; the computation of the superposition coefficients uses elementary Fourier analysis. Solutions are illustrated for various initial conditions.
ACCESSION #
9820803

 

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