Generalized Korteweg–De Vries equation

In mathematics, a 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.

References

• 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
• Bona, J., Hong, Y. Numerical Study of the Generalized Korteweg–de Vries Equations with Oscillating Nonlinearities and Boundary Conditions. Water Waves 4, 109–137 (2022). https://doi.org/10.1007/s42286-022-00057-5