### Abstract

The modified Fisher–Kolmogorov–Petrovskii–Piskunov equation with quasilocal quadratic competitive losses and variable coefficients in the small nonlocality parameter approximation is reduced to an equation with a nonlinear diffusion coefficient. Within the framework of a perturbation method, equations are obtained for the first terms of an asymptotic expansion of an approximate solution of the reduced equation. Particular solutions in separating variables are considered for the equations determining the first terms of the asymptotic series. The problem is reduced to an elliptic integral and one linear, homogeneous ordinary differential equation.

Language | English |
---|---|

Pages | 1461-1468 |

Number of pages | 8 |

Journal | Russian Physics Journal |

Volume | 60 |

Issue number | 9 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

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### Keywords

- Fisher–Kolmogorov–Petrovskii–Piskunov equation
- perturbation method
- quasilocal competitive losses
- separation of variables

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses.** / Shapovalov, A. V.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses

AU - Shapovalov, A. V.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The modified Fisher–Kolmogorov–Petrovskii–Piskunov equation with quasilocal quadratic competitive losses and variable coefficients in the small nonlocality parameter approximation is reduced to an equation with a nonlinear diffusion coefficient. Within the framework of a perturbation method, equations are obtained for the first terms of an asymptotic expansion of an approximate solution of the reduced equation. Particular solutions in separating variables are considered for the equations determining the first terms of the asymptotic series. The problem is reduced to an elliptic integral and one linear, homogeneous ordinary differential equation.

AB - The modified Fisher–Kolmogorov–Petrovskii–Piskunov equation with quasilocal quadratic competitive losses and variable coefficients in the small nonlocality parameter approximation is reduced to an equation with a nonlinear diffusion coefficient. Within the framework of a perturbation method, equations are obtained for the first terms of an asymptotic expansion of an approximate solution of the reduced equation. Particular solutions in separating variables are considered for the equations determining the first terms of the asymptotic series. The problem is reduced to an elliptic integral and one linear, homogeneous ordinary differential equation.

KW - Fisher–Kolmogorov–Petrovskii–Piskunov equation

KW - perturbation method

KW - quasilocal competitive losses

KW - separation of variables

UR - http://www.scopus.com/inward/record.url?scp=85040953533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040953533&partnerID=8YFLogxK

U2 - 10.1007/s11182-018-1236-6

DO - 10.1007/s11182-018-1236-6

M3 - Article

VL - 60

SP - 1461

EP - 1468

JO - Russian Physics Journal

T2 - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 9

ER -