Eikonal equation for a variable-speed wave
= Eikonal equation for a variable-speed wave
{title2=$\omega^2=c^2|\mathbf k|^2$}
For the <wave equation> $\varphi_{tt}-\nabla\cdot(c^2\nabla\varphi)=0$ with slow variables and phase $e^{i\theta/\varepsilon}$, define $\omega=-\theta_T$ and $\mathbf k=\nabla\theta$. The leading balance is $\omega^2=c^2|\mathbf k|^2$. Its positive-frequency <dispersion relation> is $\Omega=c|\mathbf k|$, and the <group velocity> is $c\mathbf k/|\mathbf k|$.