One-Dimensional Fokker–Planck Equation with Quadratically Nonlinear Quasilocal Drift
- Авторлар: Shapovalov A.V.1,2
-
Мекемелер:
- National Research Tomsk State University
- National Research Tomsk Polytechnic University
- Шығарылым: Том 60, № 12 (2018)
- Беттер: 2063-2072
- Бөлім: Article
- URL: https://bakhtiniada.ru/1064-8887/article/view/239808
- DOI: https://doi.org/10.1007/s11182-018-1327-4
- ID: 239808
Дәйексөз келтіру
Аннотация
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.
Авторлар туралы
A. Shapovalov
National Research Tomsk State University; National Research Tomsk Polytechnic University
Хат алмасуға жауапты Автор.
Email: shpv@phys.tsu.ru
Ресей, Tomsk; Tomsk
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