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

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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

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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)

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