Addendum to 3) of my previous posts (then I'll quit!):
For a graded index fiber with a quadratic index profile, the group velocity
is approximately equal to the axial bulk velocity (at r=0). That this
statement holds for all modes shows the (low dispersion) advantage of this
type fiber.
Note: Closed form solutions for the graded index case do not exist -
numerical/approximate methods are necessary.
A good reference is: "Fundamentals of Photonics", Saleh & Teich, J Wiley,
1991.