Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

European Journal of Applied Mathematics

ISSN

0956-7925

e-ISSN

1469-4425

Svazek periodika

34

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

1067-1098

Kód UT WoS článku

000981844100001

EID výsledku v databázi Scopus

2-s2.0-85161069056