Semiclassical approximation for the twodimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal nonlinearity in polar coordinates

Semiclassical approximation for the twodimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal nonlinearity in polar coordinates

Détails bibliographiques
Parent link:Russian Physics Journal: Scientific Journal
Vol. 53, iss. 12.— 2011.— [P. 1243-1253]
Auteur principal: Trifonov A. Yu. Andrey Yurievich
Autres auteurs: Shapovalov A. V. Aleksandr Vasilyevich
Résumé:Title screen
The two-dimensional Kolmogorov–Petrovskii–Piskunov–Fisher equation with nonlocal nonlinearity and axially symmetric coefficients in polar coordinates is considered. The method of separation of variables in polar coordinates and the nonlinear superposition principle proposed by the authors are used to construct the asymptotic solution of a Cauchy problem in a special class of smooth functions. The functions of this class arbitrarily depend on the angular variable and are semiclassically concentrated in the radial variable. The angular dependence of the function has been exactly taken into account in the solution. For the radial equation, the formalism of semiclassical asymptotics has been developed for the class of functions which singularly depend on an asymptotic small parameter, whose part is played by the diffusion coefficient. A dynamic system of Einstein–Ehrenfest equations (a system of equations in mean and central moments) has been derived. The evolution operator for the class of functions under consideration has been constructed in explicit form
Режим доступа: по договору с организацией-держателем ресурса
Langue:anglais
Publié: 2011
Sujets:
электронный ресурс
труды учёных ТПУ
nonlocal nonlinearity
нелинейность
уравнение Фишера-Колмогорова-Петровского-Пискунова
equation
semiclassical asymptotics
квазиклассическая асимптотика
Accès en ligne:http://link.springer.com/article/10.1007/s11182-011-9556-9
Format: Électronique Chapitre de livre
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=636467

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