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


Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

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

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature