Local equality of phase and group velocity
= Local equality of phase and group velocity
{title2=$v_g-v_p=k\,dv_p/dk$}
For a differentiable <dispersion relation> and nonzero <wavenumber> $k$, <group velocity> equals <phase velocity> precisely where $dv_p/dk=0$. Equality at an isolated stationary point of $v_p$ does not establish a nondispersive branch. For a <gravity-capillary wave>, the equality occurs at $k=\sqrt{\rho g/T}$ and the phase-speed minimum, even though the relation is dispersive elsewhere.