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{{Underlinked|date=August 2013}}
 
In mathematics the '''generalized Korteweg–de Vries equation''' {{harvs|
|last=Tsutsumi|first= Masayoshi|last2= Mukasa|first2= Toshio|last3= Iino|first3= Riichi|year=1970}} is the [[nonlinear partial differential equation]]
 
:<math>\partial_t u + \partial_x^3 u +  \partial_x f(u) = 0.\,</math>
The 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}}
 
==External links==
*{{dpde}}
 
{{DEFAULTSORT:Generalized Korteweg-de Vries equation}}
[[Category:Partial differential equations]]

Revision as of 22:50, 27 November 2013

Template:Underlinked

In mathematics the generalized Korteweg–de Vries equation Template:Harvs is the nonlinear partial differential equation

tu+x3u+xf(u)=0.

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.

References

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