Abstract
The exact solution to the Cauchy problem for a generalized “linear” vectorial Fokker-Planck equation is found by using the disentangling techniques of Feynman and algebraic (operational) methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. D. Fokker, Ann. der Phys. 43, 812 (1914).
M. V. Smoluchowski, Ann. der Phys. 48, 1103 (1915).
M. Planck, Sitz. Preuss. Akad. Wiss., Phys. Math. Kl., 324 (1917).
G. E. Uhlenbeck and L. S. Ornstein, Phys. Rev. 36, 823 (1930).
A. N. Kolmogorov, Math. Ann. 108, 149 (1933).
H. Kramers, Physica (Amsterdam) 7, 284 (1940).
S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).
M. C. Wang and G. E. Uhlenbeck, Rev. Mod. Phys. 17, 323 (1945).
M. Lax, Rev. Mod. Phys. 32, 25 (1960); 38, 359 (1966).
I. I. Gihman and A. V. Skorohod, Stochastic Differential Equations (Naukova Dumka, Kiev, 1968; Springer-Verlag, Berlin, 1972).
P. Hanggi and H. Thomas, Z. Phys. B 22, 295 (1975); Phys. Rep. 88, 209 (1982).
L. Ricciardi, Diffusion Processes and Related Topics in Biology (Springer-Verlag, Berlin, 1977).
N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981; Vysshaya Shkola, Moscow, 1986).
H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1989, 2nd ed.).
R. L. Kautz, Rep. Prog. Phys. 59, 935 (1996).
Y. Abe et al., Phys. Rep. 275, 49 (1996).
R. Friedrich and J. Peinke, Phys. Rev. Lett. 78, 863 (1997).
M. Suzuki, Physica A (Amsterdam) 117, 103 (1983); J. Math. Phys. (N.Y.) 26, 601 (1985).
A. N. Drozdov, Phys. Rev. E 55, 1496, 2496 (1997).
A. A. Donkov, A. D. Donkov, and E. I. Grancharova, Int. J. Mod. Phys. A 12, 165 (1997).
A. A. Donkov, A. D. Donkov, and E. I. Grancharova, Yad. Fiz. 63, 745 (2000) [Phys. At. Nucl. 63, 680 (2000)].
R. Feynman, Phys. Rev. 84, 108 (1951).
V. P. Maslov, Operational Methods (Nauka, Moscow, 1973; Mir, Moscow, 1976).
J. Kohn, Pseudodifferential Operators (Mir, Moscow, 1967) (in Russian).
L. Hörmander, Linear Partial Differential Operators (Springer-Verlag, Berlin, 1963).
Ju. A. Dubinskii, Sov. Math. Dokl. 23, 523 (1981); 38, 206 (1989).
M. E. Taylor, Pseudodifferential Operators (Princeton Univ. Press, Princeton, 1981).
Author information
Authors and Affiliations
Additional information
From Yadernaya Fizika, Vol. 65, No. 6, 2002, pp. 1049–1052.
Original English Text Copyright © 2002 by A.A. Donkov, A.D. Donkov, Grancharova.
This article was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
Donkov, A.A., Donkov, A.D. & Grancharova, E.I. Exact solution to the cauchy problem for a generalized “linear” vectorial Fokker-Planck equation: Algebraic approach. Phys. Atom. Nuclei 65, 1015–1018 (2002). https://doi.org/10.1134/1.1490101
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1490101