Cole-Hopf transformation
= Cole-Hopf transformation
{c}
{title2=$u=-2\nu\,\partial_x\log\phi$}
{wiki}
The Cole-Hopf transformation $u=-2\nu\phi_x/\phi$ converts the <viscous Burgers equation> into the <heat equation> $\phi_t=\nu\phi_{xx}$. Initial data $u(x,0)=g(x)$ correspond to $\phi(x,0)=C\exp[-(2\nu)^{-1}\int^xg(s)\,ds]$.