### Abstract

The Cauchy problem for the Fokker-Plank-Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker-Plank-Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented.

Original language | English |
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Article number | 005 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 3 |

DOIs | |

Publication status | Published - 1 Jan 2007 |

### Fingerprint

### Keywords

- Fokker-plank-kolmogorov equation
- Nonlinear partial differential equations
- Symmetry operators

### ASJC Scopus subject areas

- Analysis
- Mathematical Physics
- Geometry and Topology

### Cite this

**Symmetry operators for the Fokker-Plank-Kolmogorov equation with nonlocal quadratic nonlinearity.** / Shapovalov, Aleksandr Vasilievich; Rezaev, Roman O.; Trifonov, Andrey Yu.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Symmetry operators for the Fokker-Plank-Kolmogorov equation with nonlocal quadratic nonlinearity

AU - Shapovalov, Aleksandr Vasilievich

AU - Rezaev, Roman O.

AU - Trifonov, Andrey Yu

PY - 2007/1/1

Y1 - 2007/1/1

N2 - The Cauchy problem for the Fokker-Plank-Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker-Plank-Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented.

AB - The Cauchy problem for the Fokker-Plank-Kolmogorov equation with a nonlocal nonlinear drift term is reduced to a similar problem for the correspondent linear equation. The relation between symmetry operators of the linear and nonlinear Fokker-Plank-Kolmogorov equations is considered. Illustrative examples of the one-dimensional symmetry operators are presented.

KW - Fokker-plank-kolmogorov equation

KW - Nonlinear partial differential equations

KW - Symmetry operators

UR - http://www.scopus.com/inward/record.url?scp=84889234729&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84889234729&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2007.005

DO - 10.3842/SIGMA.2007.005

M3 - Article

AN - SCOPUS:84889234729

VL - 3

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 005

ER -