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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| Izvleček: | 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 |
| Jezik: | angleščina |
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2011
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| Teme: | |
| Online dostop: | http://link.springer.com/article/10.1007/s11182-011-9556-9 |
| Format: | Elektronski Book Chapter |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=636467 |
MARC
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| 200 | 1 | |a Semiclassical approximation for the twodimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation with nonlocal nonlinearity in polar coordinates |f A. Yu. Trifonov, A. V. Shapovalov | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [Referen.: p. 1253 (10 title)] | ||
| 330 | |a 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 | ||
| 333 | |a Режим доступа: по договору с организацией-держателем ресурса | ||
| 461 | |t Russian Physics Journal |o Scientific Journal | ||
| 463 | |t Vol. 53, iss. 12 |v [P. 1243-1253] |d 2011 | ||
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a nonlocal nonlinearity | |
| 610 | 1 | |a нелинейность | |
| 610 | 1 | |a уравнение Фишера-Колмогорова-Петровского-Пискунова | |
| 610 | 1 | |a equation | |
| 610 | 1 | |a semiclassical asymptotics | |
| 610 | 1 | |a квазиклассическая асимптотика | |
| 700 | 1 | |a Trifonov |b A. Yu. |c physicist, mathematician |c Professor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences |f 1963- |g Andrey Yurievich |3 (RuTPU)RU\TPU\pers\30754 | |
| 701 | 1 | |a Shapovalov |b A. V. |c mathematician |c Professor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences |f 1949- |g Aleksandr Vasilyevich |3 (RuTPU)RU\TPU\pers\31734 | |
| 801 | 2 | |a RU |b 63413507 |c 20150321 |g RCR | |
| 856 | 4 | |u http://link.springer.com/article/10.1007/s11182-011-9556-9 | |
| 942 | |c CF | ||