An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher–KPP equation; International Journal of Geometric Methods in Modern Physics; Vol. 15, iss. 6

An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher–KPP equation; International Journal of Geometric Methods in Modern Physics; Vol. 15, iss. 6

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Parent link:International Journal of Geometric Methods in Modern Physics: Scientific Journal
Vol. 15, iss. 6.— 2018.— [1850102, 28 p.]
Hlavní autor: Shapovalov A. V. Aleksandr Vasilyevich
Korporativní autor: Национальный исследовательский Томский политехнический университет Исследовательская школа физики высокоэнергетических процессов
Další autoři: Trifonov A. Yu. Andrey Yurievich
Shrnutí:Title screen
A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov (Fisher–KPP) equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher–KPP equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure.
Режим доступа: по договору с организацией-держателем ресурса
Jazyk:angličtina
Vydáno: 2018
Témata:
электронный ресурс
труды учёных ТПУ
Nonlocal Fisher
KPP equation
semiclassical approximation
complex germ
symmetry operators
pattern formation
On-line přístup:https://doi.org/10.1142/S0219887818501025
Médium: Elektronický zdroj Kapitola
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=666954

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