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Transformations of KdV equation

  1. Aug 5, 2007 #1
    Hi all.
    I have seen a lot of different forms of the KdV equation...
    The derivation of it results in a form like
    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..

    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.

    Please give me some clues...
  2. jcsd
  3. Aug 8, 2007 #2


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    Staff: Mentor

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


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    Staff: Mentor

    More on the KdV equation

    The General Analytical Solution for the Korteweg- de Vries Equation

    The Korteweg-de Vries Equation:
    History, exact Solutions, and graphical Representation

    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! :approve:

    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
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