Semiclassical approximation for the twodimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal nonlinearity in polar coordinates
| Parent link: | Russian Physics Journal: Scientific Journal Vol. 53, iss. 12.— 2011.— [P. 1243-1253] |
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| सारांश: | 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 |
| भाषा: | अंग्रेज़ी |
| प्रकाशित: |
2011
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| ऑनलाइन पहुंच: | http://link.springer.com/article/10.1007/s11182-011-9556-9 |
| स्वरूप: | इलेक्ट्रोनिक पुस्तक अध्याय |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=636467 |