### 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 language | English |
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Article number | 305203 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

Issue number | 30 |

DOIs | |

Publication status | Published - 15 Jun 2016 |

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### 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)