Fisher's equation

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NOTE: this is not the Fisher equation in financial mathematics.

Fisher's equation is the following partial differential equation arising in physics and biology:

ut = uxx + u − u2.

It admits travelling wave solutions given by

u(t,x) = \frac{1}{\left( 1 + C \exp(-\frac56t \pm \frac16\sqrt{6}\,x) \right)^2}

where C is an arbitrary constant.

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