Surprising Symmetry Properties and Exact Solutions of Kolmogorov Backward Equations With Power Diffusivity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F25%3AA0000188" target="_blank" >RIV/47813059:19610/25:A0000188 - isvavai.cz</a>

Výsledek na webu

<a href="https://onlinelibrary.wiley.com/doi/10.1111/sapm.70105" target="_blank" >https://onlinelibrary.wiley.com/doi/10.1111/sapm.70105</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1111/sapm.70105" target="_blank" >10.1111/sapm.70105</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Surprising Symmetry Properties and Exact Solutions of Kolmogorov Backward Equations With Power Diffusivity

Popis výsledku v původním jazyce

Using the original advanced version of the direct method, we efficiently compute the equivalence groupoids and equivalence groups of two peculiar classes of Kolmogorov backward equations with power diffusivity and solve the problems of their complete group classifications. The results on the equivalence groups are double-checked with the algebraic method. Within these classes, the remarkable Fokker–Planck and the fine Kolmogorov backward equations are distinguished by their exceptional symmetry properties. We extend the known results on these two equations to their counterparts with respect to a nontrivial discrete equivalence transformation. Additionally, we carry out Lie reductions of the equations under consideration up to the point equivalence, exhaustively study their hidden Lie symmetries, and generate wider families of their new exact solutions via acting by their recursion operators on constructed Lie-invariant solutions. This analysis reveals eight powers of the space variable with exponents -1, 0, 1, 2, 3, 4, 5, and 6 as values of the diffusion coefficient that are prominent due to symmetry properties of the corresponding equations.

Název v anglickém jazyce

Surprising Symmetry Properties and Exact Solutions of Kolmogorov Backward Equations With Power Diffusivity

Popis výsledku anglicky

Using the original advanced version of the direct method, we efficiently compute the equivalence groupoids and equivalence groups of two peculiar classes of Kolmogorov backward equations with power diffusivity and solve the problems of their complete group classifications. The results on the equivalence groups are double-checked with the algebraic method. Within these classes, the remarkable Fokker–Planck and the fine Kolmogorov backward equations are distinguished by their exceptional symmetry properties. We extend the known results on these two equations to their counterparts with respect to a nontrivial discrete equivalence transformation. Additionally, we carry out Lie reductions of the equations under consideration up to the point equivalence, exhaustively study their hidden Lie symmetries, and generate wider families of their new exact solutions via acting by their recursion operators on constructed Lie-invariant solutions. This analysis reveals eight powers of the space variable with exponents -1, 0, 1, 2, 3, 4, 5, and 6 as values of the diffusion coefficient that are prominent due to symmetry properties of the corresponding equations.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Studies in Applied Mathematics

ISSN

0022-2526

e-ISSN

1467-9590

Svazek periodika

155

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

36

Strana od-do

„e70105-1“-„e70105-36“

Kód UT WoS článku

001583209500001

EID výsledku v databázi Scopus

2-s2.0-105016092478