Group-invariant solutions of the Fokker-Planck equation

Group-invariance under infinitesimal transformations is used to generate a wide class of solutions of some Fokker-Planck equations. The partial differential equation in two variables is reduced to an ordinary differential equation; reduction of the latter to standard forms is noted in most cases. Some of the known existing solutions are obtained as particular cases. Only self-similar types of solutions are discussed. The appearance of a free parameter that can be treated as an eigenvalue (or transform variable) offers flexibility in constructing new solutions. Some solutions of this parabolic equation have wave-like features. The general results can also be used to solve some types of moving-boundary problems.