Surprising Symmetry Properties and Exact Solutions of Kolmogorov Backward Equations With Power Diffusivity
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Surprising Symmetry Properties and Exact Solutions of Kolmogorov Backward Equations With Power Diffusivity
Original language description
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.
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
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studies in Applied Mathematics
ISSN
0022-2526
e-ISSN
1467-9590
Volume of the periodical
155
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
36
Pages from-to
„e70105-1“-„e70105-36“
UT code for WoS article
001583209500001
EID of the result in the Scopus database
2-s2.0-105016092478