Generalized Korteweg–De Vries equation

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


 * $$\partial_t u + \partial_x^3 u + \partial_x f(u) = 0.\,$$

The function f is 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.