The existence of self-similar solutions of the one-dimensional Fokker-Planck equation P/t=(/x)(RP+D P/x) poses specific constraints on the shape of the drag and diffusion coefficients R(x) and D(x) as functions of the space variable x. It is shown that these constraints can be formulated in terms of a single Riccati equation which can be solved exactly. The form of the functions R(x) and D(x) leading to self-similar evolution of one-dimensional systems governed by the above Fokker-Planck equation is therefore determined in full generality. © 1987 The American Physical Society.

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