### 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.

Original language | English |
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Pages (from-to) | 118-128 |

Number of pages | 11 |

Journal | Russian Physics Journal |

Volume | 45 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 2002 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Russian Physics Journal*,

*45*(2), 118-128. https://doi.org/10.1023/A:1019639628309

**The Fokker-Planck-Kolmogorov equation with nonlocal nonlinearity in the semiclassical approximation.** / Trifonov, A. Yu; Trifonova, L. B.

Research output: Contribution to journal › Article

*Russian Physics Journal*, vol. 45, no. 2, pp. 118-128. https://doi.org/10.1023/A:1019639628309

}

TY - JOUR

T1 - The Fokker-Planck-Kolmogorov equation with nonlocal nonlinearity in the semiclassical approximation

AU - Trifonov, A. Yu

AU - Trifonova, L. B.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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(D3/2). 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.

AB - 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(D3/2). 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.

UR - http://www.scopus.com/inward/record.url?scp=14544308359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14544308359&partnerID=8YFLogxK

U2 - 10.1023/A:1019639628309

DO - 10.1023/A:1019639628309

M3 - Article

AN - SCOPUS:14544308359

VL - 45

SP - 118

EP - 128

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 2

ER -