Examples of Asymptotic Solutions Obtained by the Complex Germ Method for the One-Dimensional Nonlocal Fisher-Kolmogorov-Petrovsky-Piskunov Equation

The general construction of the Cauchy problem solution for the one-dimensional nonlocal population Fisher-KPP equation is briefly described in terms of semiclassical asymptotics based on the complex WKB-Maslov method. For the particular case of the equation under consideration, a family of leading terms of the semiclassical asymptotics is constructed in an explicit form, and their qualitative behavior is investigated. The behavior of the asymptotic solutions and of the corresponding numerical solutions constructed using the software package Comsol Multiphysics is compared.