Classification of potential symmetries of generalised inhomogeneous nonlinear diffusion equations

We consider the class of generalised nonlinear diffusion equations f(x)ut=[g(x)unux]x which are of considerable interest in mathematical physics. We classify the nonlocal symmetries, which are known as potential symmetries, for these equations. It turns out that potential symmetries exist only if the parameter n takes the values −2 or −23. Also certain relations must be satisfied by the functions f(x) and g(x). For the cases where we obtain infinite-parameter potential symmetries, linearising mappings are constructed. Furthermore we employ the potential symmetries to derive similarity solutions.