  We consider long longitudinal bulk strain waves in layered waveguides using
Boussinesq-type equations. The equations are developed using lattice models,
and this is viewed as an extension of the Fermi-Pasta-Ulam problem. We describe
semi-analytical approaches to the solution of scattering problems in
delaminated waveguides, and to the construction of the solution of an
initial-value problem in the class of periodic functions, motivated by the
scattering problems.
