Nonlinear Longitudinal Bulk Strain Waves in Layered Elastic Waveguides

Abstract

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.

Scattering of an Ostrovsky wave packet in a delaminated waveguide

“…recently, for the finite interval, the contradiction is resolved for the Boussinesq-Klein-Gordon (BKG) equation, whose leading order weakly-nonlinear solution is the Ostrovsky equation [17,23,24]. A similar contradiction is also resolved for a system of coupled Boussinesq equations when the characteristic speeds are close [25].…”