Abstract
It is generally accepted that integrable partial differential time evolution equations possess Lie-Backlund symmetries of arbitrarily high finite order. It has already been established that in (1+1) dimensions the full class of nonlinear Fokker-Planck (convection-diffusion) equations having this property consists of the known integrable examples. These are closely related either to the Burgers equations or to the Fokas-Yortsos-Rosen equation, both of which have been applied to unsaturated flow in porous media. Here the author shows that higher-order Lie-Backlund symmetries do not exist for any examples of the nonlinear Fokker-Planck equation in (1+2) (one time and two space) dimensions.
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