Abstract
In the framework of the theory of isotropic incompressible nonlinear elasticity we derive an asymptotic system of equations using a multiple scales expansion and considering waves of finite but small amplitude composed by an anti-plane shear superposed to a general plane motion. The system of equations generalizes the classical Zabolotskaya equation. Moreover, we show that the hyperbolic system, we derive, has a mathematical structure similar to the systems determining the propagation of transverse waves in nonlinear elasticity.
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