Symmetry Operators for the Fokker-Plank-Kolmogorov Equation with Nonlocal Quadratic Nonlinearity

被引：9

作者：

Shapovalov, Alexander V. ^{[1
]}

Rezaev, Roman O. ^{[2
]}

Trifonov, Andrey Yu. ^{[2
]}

机构：

[1] Tomsk State Univ, Dept Theoret Phys, Tomsk 660050, Russia

[2] Tomsk Polytech Univ, Dept Math Phys, Phys Math Lab, Tomsk 660034, Russia

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2007年 / 3卷

关键词：

symmetry operators; Fokker-Plank-Kolmogorov equation; nonlinear partial differential equations;

D O I：

10.3842/SIGMA.2007.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：16

共 24 条

[21] Symmetry operators of a Hartree-type equation with quadratic potential
A. L. Lisok
A. Yu. Trifonov
A. V. Shapovalov
Siberian Mathematical Journal, 2005, 46 : 119 - 132
[22] Semiclassically concentrated solutions for the one-dimensional Fokker-Planck equation with a nonlocal nonlinearity
Bellucci, S
Trifonov, AY
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (07): : L103 - L114
[23] Semiclassical approximation for the twodimensional Fisher–Kolmogorov–Petrovskii– Piskunov equation with nonlocal nonlinearity in polar coordinates
A. Yu. Trifonov
A. V. Shapovalov
Russian Physics Journal, 2011, 53
[24] SEMICLASSICAL APPROXIMATION FOR THE TWO-DIMENSIONAL FISHER-KOLMOGOROV-PETROVSKIIPISKUNOV EQUATION WITH NONLOCAL NONLINEARITY IN POLAR COORDINATES
Trifonov, A. Yu.
Shapovalov, A. V.
RUSSIAN PHYSICS JOURNAL, 2011, 53 (12) : 1243 - 1253

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