A system of coupled Klein-Gordon equations is suggested to model onedimensional
nonlinear wave processes in a bi-layer. The type of coupling
depends on the type of the interface and constitutes an arbitrary element
of the Lie group classification problem, which is solved for these
equations. The classification results are used to find conservation laws
and particular invariant solutions.
This is a pre-print of a paper presented at the IUTAM Symposium “Asymptotics, Singularities and Homogenisation
in Problems of Mechanics”, July 8-11, 2002, The University of Liverpool, UK.