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Can anybody see why $${d\over dt}\int_{-\infty}^\infty -f_{xx}+f^2\,\,\, dx=0$$ where $f=f(x,t)$, follows from $$f_t+f_{xxx}+6ff_x=0$$?

I tried differentiating under the integral sign, but things got ugly.

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    Where is this problem from?2012-11-10
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    I don't see how this could follow independently of the trajectory $x(t)$. Are you sure you intended that to be a total derivative with respect to time and not a partial derivative?2012-11-10
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    @joriki unfortunately so...2012-11-10
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    @martini It is from a handout I got, it is talking about 1st integrals of the [Korteweg–de_Vries_equation](http://en.wikipedia.org/wiki/Korteweg–de_Vries_equation)2012-11-10

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