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

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.