One-Dimensional Fokker–Planck Equation with Quadratically Nonlinear Quasilocal Drift / A. V. Shapovalov
Уровень набора: Russian Physics JournalЯзык: английский ; резюме, eng.Резюме или реферат: The Fokker–Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian’s iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found..Примечания о наличии в документе библиографии/указателя: [References: 18 tit.].Аудитория: .Тематика: электронный ресурс | труды учёных ТПУ | nonlinear Fokker–Planck equation | quasilocal approximation | Lie symmetries | traveling waves | Adomian decomposition method | exact solutions Ресурсы он-лайн:Щелкните здесь для доступа в онлайнTitle screen
[References: 18 tit.]
The Fokker–Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian’s iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.
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