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 |
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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)
Cite this
Asymptotics semiclassically concentrated on curves for the nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov equation. / Levchenko, Evgeniy Anatolievich; Shapovalov, Aleksandr Vasilievich; Trifonov, A. Yu.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 49, No. 30, 305203, 15.06.2016.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 -