Abstract
We have investigated the pattern formation in systems described by the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation for the cases where the dimension of the pattern concentration domain is lower than that of the domain of independent variables. We have obtained a system of integro-differential equations which describe the dynamics of the concentration domain and the semiclassically limited density distribution for a pattern in the class of trajectory concentrated functions. Also, asymptotic large time solutions have been obtained that describe the semiclassically limited distribution for a quasi-steady-state pattern on the concentration manifold. The approach is illustrated by an example for which the analytical solution is in good agreement with the results of numerical calculations.
| Original language | English |
|---|---|
| Article number | 025209 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 47 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 17 Jan 2014 |
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Keywords
- Fisher-Kolmogorov- Petrovskii-Piskunov equation
- nonlocal population dynamics
- pattern formation
- semiclassical approximation
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)
Cite this
Pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation. / Levchenko, Evgeniy Anatolievich; Shapovalov, Aleksandr Vasilievich; Trifonov, A. Yu.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 47, No. 2, 025209, 17.01.2014.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation
AU - Levchenko, Evgeniy Anatolievich
AU - Shapovalov, Aleksandr Vasilievich
AU - Trifonov, A. Yu
PY - 2014/1/17
Y1 - 2014/1/17
N2 - We have investigated the pattern formation in systems described by the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation for the cases where the dimension of the pattern concentration domain is lower than that of the domain of independent variables. We have obtained a system of integro-differential equations which describe the dynamics of the concentration domain and the semiclassically limited density distribution for a pattern in the class of trajectory concentrated functions. Also, asymptotic large time solutions have been obtained that describe the semiclassically limited distribution for a quasi-steady-state pattern on the concentration manifold. The approach is illustrated by an example for which the analytical solution is in good agreement with the results of numerical calculations.
AB - We have investigated the pattern formation in systems described by the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation for the cases where the dimension of the pattern concentration domain is lower than that of the domain of independent variables. We have obtained a system of integro-differential equations which describe the dynamics of the concentration domain and the semiclassically limited density distribution for a pattern in the class of trajectory concentrated functions. Also, asymptotic large time solutions have been obtained that describe the semiclassically limited distribution for a quasi-steady-state pattern on the concentration manifold. The approach is illustrated by an example for which the analytical solution is in good agreement with the results of numerical calculations.
KW - Fisher-Kolmogorov- Petrovskii-Piskunov equation
KW - nonlocal population dynamics
KW - pattern formation
KW - semiclassical approximation
UR - http://www.scopus.com/inward/record.url?scp=84891363627&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84891363627&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/47/2/025209
DO - 10.1088/1751-8113/47/2/025209
M3 - Article
VL - 47
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 2
M1 - 025209
ER -