= Solution
Take a stable isotropic elastic material with <mass density> $\rho>0$ and <Lamé parameters> $\lambda,\mu$, where $\mu>0$ and $3\lambda+2\mu>0$. Its <elastic stiffness tensor> is
$$
c_{ijpq}=\lambda\delta_{ij}\delta_{pq}+\mu(\delta_{ip}\delta_{jq}+\delta_{iq}\delta_{jp}),\qquad \alpha^2=\frac{\lambda+2\mu}{\rho},\quad\beta^2=\frac\mu\rho.
$$
The <P wave> is longitudinal and the <S wave> transverse. The wavefront-transport alternative and all three steps of the <Love wave> alternative are given below.
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