Vector form of Eikonal equations

Alternatively with the compact form

$$\frac{d\mbox{$\mathbf{r}$}}{ds} = c \; \mbox{\boldmath$\sigm... ...$}}{ds} = \frac {1}{c^2}\mbox{\boldmath$\nabla$}c \hskip5mm ,$$ (A.1)

the change of $ds$ by $d\tau$ allows to obtain the following Eikonal equations[13]

$$\frac{d\mbox{$\mathbf{r}$}}{d\tau} = c^2\mbox{\boldmath$\sig... ...$}}{d\tau} = \frac {1}{c}\mbox{\boldmath$\nabla$}c \hskip5mm .$$ (A.2)