### 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 |
---|---|

Article number | 305203 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

Issue number | 30 |

DOIs | |

Publication status | Published - 15 Jun 2016 |

### Fingerprint

### 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)

### Cite this

**Asymptotics semiclassically concentrated on curves for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation.** / Levchenko, Evgeniy Anatolievich; Shapovalov, Aleksandr Vasilievich; Trifonov, A. Yu.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Asymptotics semiclassically concentrated on curves for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation

AU - Levchenko, Evgeniy Anatolievich

AU - Shapovalov, Aleksandr Vasilievich

AU - Trifonov, A. Yu

PY - 2016/6/15

Y1 - 2016/6/15

N2 - 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.

AB - 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.

KW - Fisher-Kolmogorov-Petrovskii-Piskunov equation

KW - quasi-steady-state solution

KW - semiclassical approximation

UR - http://www.scopus.com/inward/record.url?scp=84978910542&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84978910542&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/49/30/305203

DO - 10.1088/1751-8113/49/30/305203

M3 - Article

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 30

M1 - 305203

ER -