Generalized Korteweg–De Vries equation explained

In mathematics, a generalized Korteweg–De Vries equation is the nonlinear partial differential equation

\partialtu+

3
\partial
x

u+\partialxf(u)=0.

The function fis sometimes taken to be f(u) = uk+1/(k+1) + u for some positive integer k (where the extra u is a "drift term" that makes the analysis a little easier). The case f(u) = 3u2 is the original Korteweg–De Vries equation