Solution
= Solution
Differentiate the positive-frequency <dispersion relation> with respect to $k$:
$$
\boxed{c_g=\frac{d\omega}{dk}=\frac{c^2k}{\sqrt{c^2k^2+a}}=\frac{c^2k}{\omega}.}
$$
Where $k\ne0$, $c_pc_g=c^2$. For $a>0$ and $c\ne0$, the magnitude of the <group velocity> is below $|c|$ even though the positive-$k$ <phase velocity> exceeds $|c|$. At $k=0$, the group velocity is zero. The two velocities describe envelope and phase transport, respectively.