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.