The Einstein−Ehrenfest system of (0, M)-type and asymptotical solutions of the multidimensional nonlinear Fokker−Planck−Kolmogorov equation

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Semiclassical approximation formalism is developed for the multidimensional Fokker–Planck–Kolmogorov equation with non-local and nonlinear drift vector with respect to a small diffusion coefficient D, D→0, in the class of trajectory concentrated functions. The Einstein−Ehrenfest system of (0, M)-type is obtained. A family of semiclassical solutions localized around a point driven by the Einstein−Ehrenfest system accurate to O(D(M+1)/2) is found.

Keywords: nonlinear Fokker−Planck−Kolmogorov equation, semiclassical asymptotics, WKB-Maslov method, Einstein−Ehrenfest system
Citation in English: Rezaev R.O., Trifonov A.Y., Shapovalov A.V. The Einstein−Ehrenfest system of (0, M)-type and asymptotical solutions of the multidimensional nonlinear Fokker−Planck−Kolmogorov equation // Computer Research and Modeling, 2010, vol. 2, no. 2, pp. 151-160
Citation in English: Rezaev R.O., Trifonov A.Y., Shapovalov A.V. The Einstein−Ehrenfest system of (0, M)-type and asymptotical solutions of the multidimensional nonlinear Fokker−Planck−Kolmogorov equation // Computer Research and Modeling, 2010, vol. 2, no. 2, pp. 151-160
DOI: 10.20537/2076-7633-2010-2-2-151-160
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