Hey,

I've just finished a course on partial differential equations that didn't cover non-linear PDE's. With a linear PDE, I have solved by letting say

$\displaystyle u(x,t) = v(x) + w(x,t)$

or by separation of variables:

$\displaystyle u = XT$

or the method of eigenvalue expansion. Do these methods still work for non-linear PDE's? If not, are there general methods used to solve non-linear pdes?