Generalized Korteweg–de Vries equation

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In mathematics, a generalized Korteweg–de Vries equation (Masayoshi Tsutsumi, Toshio Mukasa & Riichi Iino 1970) is the nonlinear partial differential equation

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.


  • Tsutsumi, Masayoshi; Mukasa, Toshio; Iino, Riichi (1970), "On the generalized Korteweg–de Vries equation", Proc. Japan Acad., 46 (9): 921–925, doi:10.3792/pja/1195520159, MR 0289973

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