Generalized Korteweg–De Vries equation

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

${\partial }_{t}u+\underset{x}{\overset{3}{\partial }}u+{\partial }_{x}f(u)=0.$

The function f is 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.

References

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