Examples of asymptotic solutions obtained by the complex growth method for the one-dimensional nonlocal Fischer - Kolmogorov - Petrovsky - Piskunov equation
The general construction of the Cauchy problem solution in terms of semiclassical asymptotics based on the complex WKB-Maslov method is briefly described for the one-dimensional nonlocal population Fisher - KPP equation. For the particular case of the equation under consideration, a family of principal terms of semiclassical asymptotics is constructed in explicit form and their qualitative behavior is investigated. A comparison is made between the behavior of asymptotic solutions and the corresponding numerical solutions constructed using the Comsol Multiphysics software package.
Download file
Counter downloads: 30
Keywords
nonlocal Fisher - Kolmogorov - Petrovsky - Piskunov equation, semiclassical asymptotics, numerical solutionsAuthors
| Name | Organization | |
| Siniukov S.A. | National Research Tomsk State University | ssaykmh@yandex.ru |
| Trifonov A.Yu. | National Research Tomsk Polytechnic University | atifonov@tpu.ru |
| Shapovalov A.V. | National Research Tomsk State University; National Research Tomsk Polytechnic University | shpv@phys.tsu.ru |
References
Трифонов А.Ю., Шаповалов А.В. // Изв. вузов. Физика. - 2009. - Т. 52. - № 9. - С. 14-23.
Shapovalov A.V. and Trifonov A.Yu. // Int. J. Geometric Methods Mod. Phys. - 2018. - V. 15. - No. 6. - P. 1850102 (30 p).
Маслов В.П. Комплексный метод ВКБ в нелинейных уравнениях. - М.: Наука, 1977. - 384 с.
Белов В.В., Доброхотов С.Ю. // ТМФ. - 1988. - Т. 92. - № 2. - С. 215-254.
Fisher R.A. // Annu. Eugenics. - 1937. - V. 7. - No. 3. - P. 255-369.
Колмогоров А.Н., Петровский Н.Г., Пискунов Н.С. // Бюллетень МГУ. Сер. А. Математика и механика. - 1937. - Т. 1. - № 6. - С. 1-16.
Levchenko E.A., Shapovalov A.V., and Trifonov A.Yu. // J. Phys. A: Math. Theor. - 2016. - V. 49. - No. 305203 (17 p).
