Transformations of KdV equation

1. Aug 5, 2007

hanson

Hi all.
I have seen a lot of different forms of the KdV equation...
The derivation of it results in a form like
Ut+Ux+epsilon(UUx+Uxxx)=0
and after some transformation, the epsilon is removed the equation becomes
Ut+Ux+UUx+Uxxx=0, and, still, after some sort of transformation, it becomes the standard KdV..
Ut+6UUx+Uxxx=0

I just don't know what the physical meaning of these transformation is...
Sometimes the times scale is magnified, what does it mean? does it mean the solitary wave have to be observed in a fast motion or what?
So many doubts.
I am wondering if someone can write a full paragraph explaining the meanings of individual transformation and the form of KdV arrived by that transformation.

2. Aug 8, 2007

Staff: Mentor

Last edited: Aug 8, 2007
3. Aug 9, 2007

Staff: Mentor

More on the KdV equation

The General Analytical Solution for the Korteweg- de Vries Equation
http://home.usit.net/~cmdaven/korteweg.htm

The Korteweg-de Vries Equation:
History, exact Solutions, and graphical Representation
http://people.seas.harvard.edu/~jones/solitons/pdf/025.pdf

Should be interesting to compare the first with the second.

R. VICTOR JONES - http://people.seas.harvard.edu/~jones/#biblio
Robert L. Wallace Research Professor of Applied Physics in the Division of Engineering and Applied Sciences , Harvard University
Teaching since 1957! WOW!

RVJ's Soliton page - http://people.seas.harvard.edu/~jones/solitons/solitons.html

Then there is - http://planetmath.org/encyclopedia/KortewegDeVriesEquation.html

http://www.ams.org/tran/2005-357-05/S0002-9947-04-03726-2/home.html - need to register with American Mathematical Society