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What is weakly nonlinearity?

  1. Apr 6, 2007 #1
    Hi all.
    I am reading things about wave theory.
    I am rather confused about the term "weakly nonlinear".
    Say for the KdV equation:
    u_t + 6uu_x + u_xxx = 0
    This shall be a nonlinear equation due to the term uu_x, right?
    Is it a "weakly nonlinear" equation or what?
    Is "weakly nonlinear" something related to the derivation of the KdV equation or that's something related to the way we solve this nonlinear equation?
    I read a book which use a perturbation method to solve this equation, and it assume u to have a perturbtive expansion as follows:
    u = eu1 + e^2u2 + e^3u3 + ....where e is the small perturbation.

    Why don't it assumes
    u = u0 + eu1 + e^2u2 + e^3u3 + ....?

    Is there anything to do with "weakly nonlinearity"?

    Please help.
  2. jcsd
  3. Apr 6, 2007 #2
    Math forum maybe ? :wink:
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