ON THE REMARKABLE NON-LINEAR DIFFUSION EQUATION (DELTA-DELTA-X)(A(U+B)-2(DELTA-U-DELTA-X))-(DELTA-U-DELTA-T) = 0

We study the invariance properties (in the sense of Lie-Bäcklund groups) of the nonlinear diffusion equation (∂/∂curisve Greek chi)[C (u)(∂u/∂cursive Greek chi)] - (∂u/∂t ) = 0. We show that an infinite number of one-parameter Lie-Bäcklund groups are admitted if and only if the conductivity C (u) = a(u + b)-2. In this special case a one-to-one transformation maps such an equation into the linear diffusion equation with constant conductivity, (∂2ū/∂cursive Greek chī2) - (∂ū/∂t̄) = 0. We show some interesting properties of this mapping for the solution of boundary value problems. © 1980 American Institute of Physics.