Asymptotics semiclassically concentrated on curves for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation

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3 Citations (Scopus)

Abstract

In this paper we construct asymptotic solutions for the nonlocal multidimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation in the class of functions concentrated on a one-dimensional manifold (curve) using a semiclassical approximation technique. We show that the construction of these solutions can be reduced to solving a similar problem for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov in the class of functions concentrated at a point (zero-dimensional manifold) together with an additional operator condition. The general approach is exemplified by constructing a two-dimensional two-parametric solution, which describes quasi-steady-state patterns on a circumference.

Original languageEnglish
Article number305203
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number30
DOIs
Publication statusPublished - 15 Jun 2016

Keywords

  • Fisher-Kolmogorov-Petrovskii-Piskunov equation
  • quasi-steady-state solution
  • 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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