### Abstract

The classical group analysis approach used to study the symmetries of integro-differential equations in a semiclassical approximation is considered for a class of nearly linear integro-differential equations. In a semiclassical approximation, an original integro-differential equation leads to a finite consistent system of differential equations whose symmetries can be calculated by performing standard group analysis.The approach is illustrated by the calculation of the Lie symmetries in explicit form for a special case of the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov population equation.

Original language | English |
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Pages (from-to) | 716-726 |

Number of pages | 11 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 395 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Nov 2012 |

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### Keywords

- Fisher-Kolmogorov-Petrovskii-Piskunov equation
- Integro-differential equation
- Lie symmetries
- Nearly linear equation
- Semiclassical approximation

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*395*(2), 716-726. https://doi.org/10.1016/j.jmaa.2012.05.086

**Symmetries of the Fisher-Kolmogorov-Petrovskii-Piskunov equation with a nonlocal nonlinearity in a semiclassical approximation.** / Levchenko, Evgeniy Anatolievich; Shapovalov, Aleksandr Vasilievich; Trifonov, A. Yu.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 395, no. 2, pp. 716-726. https://doi.org/10.1016/j.jmaa.2012.05.086

}

TY - JOUR

T1 - Symmetries of the Fisher-Kolmogorov-Petrovskii-Piskunov equation with a nonlocal nonlinearity in a semiclassical approximation

AU - Levchenko, Evgeniy Anatolievich

AU - Shapovalov, Aleksandr Vasilievich

AU - Trifonov, A. Yu

PY - 2012/11/15

Y1 - 2012/11/15

N2 - The classical group analysis approach used to study the symmetries of integro-differential equations in a semiclassical approximation is considered for a class of nearly linear integro-differential equations. In a semiclassical approximation, an original integro-differential equation leads to a finite consistent system of differential equations whose symmetries can be calculated by performing standard group analysis.The approach is illustrated by the calculation of the Lie symmetries in explicit form for a special case of the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov population equation.

AB - The classical group analysis approach used to study the symmetries of integro-differential equations in a semiclassical approximation is considered for a class of nearly linear integro-differential equations. In a semiclassical approximation, an original integro-differential equation leads to a finite consistent system of differential equations whose symmetries can be calculated by performing standard group analysis.The approach is illustrated by the calculation of the Lie symmetries in explicit form for a special case of the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov population equation.

KW - Fisher-Kolmogorov-Petrovskii-Piskunov equation

KW - Integro-differential equation

KW - Lie symmetries

KW - Nearly linear equation

KW - Semiclassical approximation

UR - http://www.scopus.com/inward/record.url?scp=84864024328&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864024328&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2012.05.086

DO - 10.1016/j.jmaa.2012.05.086

M3 - Article

VL - 395

SP - 716

EP - 726

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -