Abstract
A scheme for constructing quasi-classical concentrated solutions of the Fokker–Planck–Kolmogorov equation with local nonlinearity is presented on the basis of the complex WKB-Maslov method. Formal, asymptotic in a series expansion parameter D, D → 0 solutions of the Cauchy problem for this equation are constructed with a power accuracy O(D 3/2). A set of the Hamilton–Ehrenfest equations (a set of equations for average and centered moments) derived in this work is of considerable importance in construction of these solutions. An approximate Green's function is constructed and a nonlinear principle of superposition is formulated in the class of semiclassical concentrated solutions of the Fokker–Planck–Kolmogorov equations.
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Trifonov, A.Y., Trifonova, L.B. The Fokker–Planck–Kolmogorov Equation with Nonlocal Nonlinearity in the Semiclassical Approximation. Russian Physics Journal 45, 118–128 (2002). https://doi.org/10.1023/A:1019639628309
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DOI: https://doi.org/10.1023/A:1019639628309