Potential symmetries and invariant solutions for the inhomogeneous nonlinear diffusion equation

The work reported here is a sequel to our paper (Physica A 304 (2002) 395), wherein we have obtained the invariant solutions of the generalized one-dimensional Fokker–Planck equation via the so-called potential symmetry method. Herein, the application of the same method has been carried over to the inhomogeneous nonlinear diffusion (INLD) equation to obtain the determining equations in most general form, which determine the one-parameter transformation group. To get the invariant solutions in explicit form, we confine our attention to the physically interesting situations. This study has led us to some new exact solutions, that does not seem to have been reported in the literature.