Generalized Korteweg–De Vries equation explained

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

\partial _{t} u + \partial ^{3} _{x} u + \partial _{x} f(u) = 0 . The function fis sometimes taken to be f(u) = u^k+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