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- W1999125280 abstract "Group theoretic methods are used to construct new exact solutions for the one-dimensional Fokker-Planck equation corresponding to a class of non-linear forcing functions f(x). An important sub-class, corresponding to f(x) = αx + βx, α 〈 1,β 〉 0 is shown to lead to stable solutions. A discussion is given on how generalized similarity methods could be applied to higher dimensional systems. On utilise des méthodes de la théorie des groupes pour construire de nouvelles solutions exactes de l'équation de Fokker-Planck à une dimension correspondant à une classe de fonctions du second membre non linéaires f(x). On montre qu'une sous classe importante correspondant à f(x) = αx + βx, α 〈 1, β 〉 0, conduit à des solutions stables. On discute comment on pourrait appliquer des méthodes de similitude généralisées à des systèmes de dimensions plus élevées. Methoden der Gruppentheorie werden benützt, um neue exakte Lösungen für die eindimensionale Fokker-Planck Gleichung, die einer Klasse von nichtlinearen Druckfunktionen ‖(x) entspricht, zu bestimmen. Es wird gezeigt, dass eine wichtige Untergruppe, für die f(x) = αx + βx,α 〈 1, β 〉 0, zu stabilen Lösungen führt Es wird diskutiert, in welcher Weise verallgemeinerte Ähnlichkeitsmethoden für höherdimensionale Systeme angewendet werden könnten. Пrимeняютsя мeтoды тeorии гruпп s цeлыu uosтroeния нoвыч тochныч reшeний oднoмerнoгo uraвнeния Фoккer-Плaнкa, sooтвeтsтвuющич клassu нeлинeйныч вынuждaaщич фuякций f(x). Пoкaзывaeтsя, chтo вaжный пoдклass sooтвeтsтвuuщий f(x) = αx + βx α 〈 1, β 〉 0 вeдÿeт к usтoйchивым reшeниям. Пrивoдитsя диsкussию пo пoвoдu тoгo, кaк oбoбщeнныe мeтoды пoдoбия мoгuт иrимeнятьsя в sлuchae sиsтeм выsшeй raзмerнosти." @default.
- W1999125280 created "2016-06-24" @default.
- W1999125280 creator A5029337066 @default.
- W1999125280 date "1971-03-01" @default.
- W1999125280 modified "2023-09-26" @default.
- W1999125280 title "Similarity solutions of the one-dimensional fokker-planck equation" @default.
- W1999125280 cites W2003995891 @default.
- W1999125280 cites W2319769735 @default.
- W1999125280 doi "https://doi.org/10.1016/0020-7462(71)90051-5" @default.
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