View source for Generalized Korteweg–De Vries equation

In [[Mathematics|mathematics]], a '''generalized Korteweg–De Vries [[Equation|equation]]''' {{harvs|
|last=Tsutsumi|first= Masayoshi|last2= Mukasa|first2= Toshio|last3= Iino|first3= Riichi|year=1970}} is the [[Nonlinear partial differential equation|nonlinear partial differential equation]]

:<math>\partial_t u + \partial_x^3 u +  \partial_x f(u) = 0.\,</math>
The [[Function (mathematics)|function]] ''f''
is sometimes taken to be  ''f''(''u'') = ''u''<sup>''k''+1</sup>/(''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'') = 3''u''<sup>2</sup> is the original [[Korteweg–De Vries equation]].

==References==
*{{citation|mr=0289973
|last=Tsutsumi|first= Masayoshi|last2= Mukasa|first2= Toshio|last3= Iino|first3= Riichi
|title=On the generalized Korteweg–De Vries equation
|journal=Proc. Japan Acad. |volume=46 |year=1970 |pages=921–925|doi=10.3792/pja/1195520159|issue=9|doi-access=free}}

{{DEFAULTSORT:Generalized Korteweg-De Vries equation}}
[[Category:Partial differential equations]]



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