Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-10 |
| Number of pages | 10 |
| Journal | Russian Physics Journal |
| Volume | 60 |
| Issue number | 12 |
| DOIs | |
| Publication status | Accepted/In press - 18 Apr 2018 |
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Keywords
- Adomian decomposition method
- exact solutions
- Lie symmetries
- nonlinear Fokker–Planck equation
- quasilocal approximation
- traveling waves
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
One-Dimensional Fokker–Planck Equation with Quadratically Nonlinear Quasilocal Drift. / Shapovalov, A. V.
In: Russian Physics Journal, Vol. 60, No. 12, 18.04.2018, p. 1-10.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - One-Dimensional Fokker–Planck Equation with Quadratically Nonlinear Quasilocal Drift
AU - Shapovalov, A. V.
PY - 2018/4/18
Y1 - 2018/4/18
N2 - 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.
AB - 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.
KW - Adomian decomposition method
KW - exact solutions
KW - Lie symmetries
KW - nonlinear Fokker–Planck equation
KW - quasilocal approximation
KW - traveling waves
UR - http://www.scopus.com/inward/record.url?scp=85045419821&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85045419821&partnerID=8YFLogxK
U2 - 10.1007/s11182-018-1327-4
DO - 10.1007/s11182-018-1327-4
M3 - Article
VL - 60
SP - 1
EP - 10
JO - Russian Physics Journal
JF - Russian Physics Journal
SN - 1064-8887
IS - 12
ER -