Generalized Korteweg–De Vries equation explained
In mathematics, a generalized Korteweg–De Vries equation is the nonlinear partial differential equation
\partialtu+
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) = 3
u2 is the original
Korteweg–De Vries equation