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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.

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# What is weakly nonlinearity?

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