Steklov Institute of Mathematics at St.Petersburg

PREPRINT 09/2007

NEW EXACT SOLUTIONS  DESCRIBING
PROPAGATION  OF ACOUSTIC SURFACE WAVES   IN ARBITRARY LAYERED STRUCTURES   

This preprint was accepted July 6, 2007

ABSTRACT:
New exact solutions, describing acoustic surface waves propagation on
an arbitrarily layered structures are constructed via a straightforward 
separation of variables. Attention is paid to solutions of 
a moderate growth in lateral variables,  $x$ and $y$, of which two 
particular cases are considered in detail. First, these are 
solutions with a plane wavefront $x=const$, but with polynomial
dependencies of amplitudes on $x$ and $y$. Second, these are
solutions describing beams of surface waves exhibiting  a high
degree of localisation inside a given sector. Dependencies of
such a wave fields on parameters are demonstrated by a
numerical simulation. Also, solutions which are inhomogeneous
plane  waves with respect to lateral variables and their
polynomial-amplitude generalisatios are considered.