Slow variables in Nonlinear Schrodinger Equation

[hanson]

Hi all.
What do it mean by "slow variables" in NLS?
I am reading a derivation of the NLS in the context of hydrodynamics, by R.S.John in his book "A modern introduction to the Mathematical Theory of Water Waves".

In the book, slow variables are zeta = epsilon * (x-ct) and T = epsilon * t.
It is counter-intuitive to me...
It seems that when epsilon is very small, the reference frame in the new time T shall observes a much faster motion then in the frame of t, right?

Why is it called "slow variables"?

What is "slow modulation of the wave packets" by the way?

 

[HallsofIvy]

This isn't really a mathematics question. I'm moving it to "Physics- Quantum Theory" where it may get more replies.

What it means, of course, is coefficients in the equation that are changing slowly enough that, in the first approximation, they can be taken to be constant.

 

[hanson]

changing coefficients? I still don't quite get it...