Relation between refractive index and model equation

[shally]

Fact: The refractive index depends on the medium.
Also, in general, to study the pulse propagation in a medium, there is a governing model equation (e.g. Non linear Schrödinger equation).

My question is: Will there be any relation between the model equation and the refractive index? Why?

Thanks and Regards,
Shally

 

[Simon Bridge]

What does refractive index tell you? i.e. what is it?
Can you extract that same information from the pulse-propagation study using the governing model equation?