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On separable Fokker-Planck equations with a constant diagonal diffusion matrix

Alexander Zhalij
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Abstract

We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec x),B_3(\vec x)$ providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients $\vec B(\vec x)$ must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructed

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Alexander Zhalij. 1999-11-12. On separable Fokker-Planck equations with a constant diagonal diffusion matrix. https://doi.org/10.1088/0305-4470%2F32%2F42%2F311

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