Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses
- Authors: Shapovalov A.V.1,2
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Affiliations:
- National Research Tomsk State University
- National Research Tomsk Polytechnic University
- Issue: Vol 60, No 9 (2018)
- Pages: 1461-1468
- Section: Elementary Particle Physics and Field Theory
- URL: https://bakhtiniada.ru/1064-8887/article/view/239279
- DOI: https://doi.org/10.1007/s11182-018-1236-6
- ID: 239279
Cite item
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.
About the authors
A. V. Shapovalov
National Research Tomsk State University; National Research Tomsk Polytechnic University
Author for correspondence.
Email: shpv@phys.tsu.ru
Russian Federation, Tomsk; Tomsk
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