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 |
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Article number | 025209 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 47 |
Issue number | 2 |
DOIs | |
Publication status | Published - 17 Jan 2014 |
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)