Pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation

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8 Citations (Scopus)

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 languageEnglish
Article number025209
JournalJournal of Physics A: Mathematical and Theoretical
Volume47
Issue number2
DOIs
Publication statusPublished - 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)

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