Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F23%3AA0000141" target="_blank" >RIV/47813059:19610/23:A0000141 - isvavai.cz</a>
Result on the web
<a href="https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/abs/extended-symmetry-analysis-of-remarkable-12dimensional-fokkerplanck-equation/C825941B001CE386DC5A1D96F86CA101" target="_blank" >https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/abs/extended-symmetry-analysis-of-remarkable-12dimensional-fokkerplanck-equation/C825941B001CE386DC5A1D96F86CA101</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0956792523000074" target="_blank" >10.1017/S0956792523000074</a>
Alternative languages
Result language
angličtina
Original language name
Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation
Original language description
We carry out the extended symmetry analysis of an ultraparabolic Fokker–Planck equation with three independent variables, which is also called the Kolmogorov equation and is singled out within the class of such Fokker–Planck equations by its remarkable symmetry properties. In particular, its essential Lie invariance algebra is eight-dimensional, which is the maximum dimension within the above class. We compute the complete point symmetry pseudogroup of the Fokker–Planck equation using the direct method, analyse its structure and single out its essential subgroup. After listing inequivalent one- and two-dimensional subalgebras of the essential and maximal Lie invariance algebras of this equation, we exhaustively classify its Lie reductions, carry out its peculiar generalised reductions and relate the latter reductions to generating solutions with iterative action of Lie-symmetry operators. As a result, we construct wide families of exact solutions of the Fokker–Planck equation, in particular, those parameterised by an arbitrary finite number of arbitrary solutions of the (1+1)-dimensional linear heat equation. We also establish the point similarity of the Fokker–Planck equation to the (1+2)-dimensional Kramers equations whose essential Lie invariance algebras are eight-dimensional, which allows us to find wide families of exact solutions of these Kramers equations in an easy way.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
European Journal of Applied Mathematics
ISSN
0956-7925
e-ISSN
1469-4425
Volume of the periodical
34
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
32
Pages from-to
1067-1098
UT code for WoS article
000981844100001
EID of the result in the Scopus database
2-s2.0-85161069056