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

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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References in corpus (2)

• On the new approach to variable separation in the time-dependent Schrödinger equation with two space dimensions
• On separable Schrödinger equations

Cited by in corpus (1)

• Separable unsteady nonparallel flow stability problems