$u_{t t}=\alpha^{2} u_{x x}+\beta^{2} u_{z z}+\left(\alpha^{2}-\beta^{2}\right) w_{x z}$
$w_{t t}=\beta^{2} w_{x x}+\alpha^{2} w_{z z}+\left(\alpha^{2}-\beta^{2}\right) u_{x z}$
were $u$ and $w$ are the horizontal and vertical displacements of each point in the medium, $\alpha$ is the velocity of the logitudinal wave, $\beta$ is the velocity of the transverse wave.
what are the physical meaning of each term?