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

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)1461-1468
Number of pages8
JournalRussian Physics Journal
Volume60
Issue number9
DOIs
Publication statusPublished - 1 Jan 2018

Fingerprint

asymptotic series
elliptic functions
differential equations
diffusion coefficient
perturbation
expansion
coefficients
approximation

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

@article{93514501b381444dbd5d38ba5bc882c6,
title = "Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses",
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.",
keywords = "Fisher–Kolmogorov–Petrovskii–Piskunov equation, perturbation method, quasilocal competitive losses, separation of variables",
author = "Shapovalov, {A. V.}",
year = "2018",
month = "1",
day = "1",
doi = "10.1007/s11182-018-1236-6",
language = "English",
volume = "60",
pages = "1461--1468",
journal = "Russian Physics Journal",
issn = "1064-8887",
publisher = "Consultants Bureau",
number = "9",

}

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

JF - Russian Physics Journal

SN - 1064-8887

IS - 9

ER -