%0 Journal Article
%T Pattern formation in terms of semiclassically limited distribution on lower-dimensional manifolds for nonlocal Fisher--Kolmogorov--Petrovskii--Piskunov equation
%A E. A. Levchenko
%A A. V. Shapovalov
%A A. Yu Trifonov
%J Physics
%D 2013
%I arXiv
%R 10.1088/1751-8113/47/2/025209
%X 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 area is less than that of independent variables space. We have obtained a system of integro-differential equations which describe the dynamics of the concentration area and the semiclassically limited distribution of a pattern in the class of trajectory concentrated functions. Also, asymptotic large-time solutions have been obtained that describe the semiclassically limited distribution of 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 prediction of a numerical simulation.
%U http://arxiv.org/abs/1306.3765v1