Slow variables in Nonlinear Schrodinger Equation

1. Aug 2, 2007

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?

2. Aug 2, 2007

HallsofIvy

Staff Emeritus
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.

3. Aug 2, 2007

hanson

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