The problem of edge wave propagation in a thin pre-stressed, incompressible elastic plate is investigated. We begin by considering the dispersion relation associated with harmonic waves propagating in an infinite plate composed of such material. In particular, symmetric modes are considered and two finite (in general non-zero) long wave speed limits shown to exist. Asymptotic integration is then carried out to derive an approximate model for this so-called symmetric long wave low frequency motion. This model involves a coupled system of two equations in two functions which we term long wave governing extensions. Two dimensional motions associated with this system are investigated and an analogue of the strong ellipticity condition, guaranteeing reality of the long wave limiting quasi-front speeds, is established. In a parallel way to previous investigations of the existence of surface wave, the existence of edge waves is then investigated. Particularly explicit results will be presented for certain pre-stressed states and strain energy functions.
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