Solitary surface transverse waves on an elastic substrate coated with a thin film

Publisher Website
Google Scholar
Abstract
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 Schrödinger equation at the interface, thus providing solutions which are the mechanical analogs of optical solitons known to propagate in nonlinear optical fibers.

This publication has 33 references indexed in Scilit: