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 language | English |
|---|---|
| Pages (from-to) | 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.
In: Russian Physics Journal, Vol. 60, No. 9, 01.01.2018, p. 1461-1468.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
JF - Russian Physics Journal
SN - 1064-8887
IS - 9
ER -