A general method recently developed to establish the conditions for the existence of similarity solutions of the Fokker-Planck-Smoluchowsky equation is applied to the one-dimensional equation P/t=(/x)[R(x)P +D(x)(P/x)]. The case of power-law behavior of the coefficient functions R(x) and D(x) is investigated in detail, and a few classes of similarity solutions are presented. In addition, a class of functions R(x) and D(x) is identified such that the general method, based on the invariance under a continuous group of transformations, is equivalent to a generalized scale transformation of the space and time variables. © 1986 The American Physical Society.

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