title: Generalized Korteweg–De Vries equation
text: # 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) = $3u^2$ is the original Korteweg–De Vries equation.
  
  