Generalized Korteweg-de Vries equation

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In mathematics the generalized Korteweg-de Vries equation (Masayoshi Tsutsumi, Toshio Mukasa & Riichi Iino 1970) 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)= 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.

[edit] References

Tsutsumi, Masayoshi; Mukasa, Toshio & Iino, Riichi (1970), “On the generalized Korteweg-de Vries equation.”, Proc. Japan Acad. 46: 921--925, MR 0289973