= Bistable cubic reaction-diffusion equation
{title2=$u_t=Du_{xx}+u(1-u)(u-r)$}
The scalar equation $u_t=Du_{xx}+u(1-u)(u-r)$ with $D>0$ and $0<r<1$ has two stable homogeneous phases $u=0,1$ and an unstable intervening equilibrium $u=r$. Indeed the reaction derivatives at these three equilibria are $-r$, $-(1-r)$ and $r(1-r)$, respectively. A <travelling wave> can connect the two stable phases. At the equal-depth value $r=1/2$, its decreasing <heteroclinic orbit> is stationary. Away from this value the phases have unequal potential depths and the front propagates.
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