E. A. Levchenko, A. Yu. Trifonov, A. V. Shapovalov, “Large-time asymptotic solutions of the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation”, Computer Research and Modeling, 2013, Volume 5, Issue 4,Pages <nobr>543

This article is cited in 2 papers

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Large-time asymptotic solutions of the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation

E. A. Levchenko^a, A. Yu. Trifonov^ab, A. V. Shapovalov^ab

^a Laboratory of Mathematical Physics of Mathematical Physics Department, Tomsk Polytechnic University, 30 Lenin ave., Tomsk, 634050, Russia
^b Theoretical Physics Department, Tomsk State University, 36 Lenin ave., Tomsk, 634050, Russia

Abstract: Asymptotic solutions are constructed for the 1D nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation. Such solutions allow to describe the quasi-steady-state patterns. Similar asymptotic solutions of the dynamical Einstein–Ehrenfest system for the 2D Fisher–Kolmogorov–Petrovskii–Piskunov equation are found. The solutions describe properties of 2D patterns localized on 1D manifolds.

Keywords: nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation, asymptotic solution, pattern formation, Einstein—Ehrenfest system.

UDC: 519.8

Received: 30.05.2013
Revised: 03.07.2013

DOI: 10.20537/2076-7633-2013-5-4-543-558