SOLITARY SURFACE TRANSVERSE-WAVES ON AN ELASTIC SUBSTRATE COATED WITH A THIN-FILM

A proof is given of the existence of stable guided solitary surface acoustic waves propagating in the form of envelope solitons on a structure made of a nonlinear substrate and a superimposed linear elastic thermodynamical interface (a very thin film) of mathematically vanishing thickness. A thin gold film on top of a lithium niobate substrate is such a system. The mathematical analysis starting with the theory of material interfaces is carried by using the Whitham-Newell technique of treatment of nonlinear, dispersive, small-amplitude, almost monochromatic waves. In the process, "wave-action" conservation equations and "dispersive" nonlinear dispersion relations are established for this type of surface waves that could also be approached by using Whitham's averaged-Lagrangian technique as modified by Hayes to account for the transverse-modal behavior. It is shown that the whole problem is reduced to studying a single nonlinear Schrodinger equation at the interface, thus providing solutions which are the mechanical analogs of optical solitons known to propagate in nonlinear optical fibers.