# Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

@article{Destrade2010ScalarEE, title={Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations}, author={Michel Destrade and Alain Goriely and Giuseppe Saccomandi}, journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, year={2010}, volume={467}, pages={1823 - 1834} }

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy–Green strain). However, we show that the Z equation…

## 19 Citations

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