A remarkable generalization of the Zabolotskaya equation. (October 2018) - Pucci, Edvige; Saccomandi, Giuseppe
Highlights: An asymptotic equation for nonlinear wave propagation is obtained. The equation is a generalization of the Z-equation. The mathematical structure is investigate and we find that waves of permanent form are possible solution. 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.