Mapping method of group classification

@article{65305,
   author = {Opanasenko, Stanislav and Popovych, Roman},
   article_location = {San Diego (USA)},
   article_number = {2},
   doi = {http://dx.doi.org/10.1016/j.jmaa.2022.126209},
   keywords = {Lie symmetries; Group classification; Mapping method; Weakly similar classes; Fokker-Planck equations; Kolmogorov equations},
   language = {eng},
   issn = {0022-247X},
   journal = {Journal of Mathematical Analysis and Applications},
   title = {Mapping method of group classification},
   url = {https://www.sciencedirect.com/science/article/pii/S0022247X22002232},
   volume = {513},
   year = {2022}
}

TY  - JOUR
ID  - 65305
AU  - Opanasenko, Stanislav - Popovych, Roman
PY  - 2022
TI  - Mapping method of group classification
JF  - Journal of Mathematical Analysis and Applications
VL  - 513
IS  - 2
SP  - "126209-1"-"126209-43"
EP  - "126209-1"-"126209-43"
PB  - Academic Press Inc. Elsevier Science
SN  - 0022247X
KW  - Lie symmetries
KW  - Group classification
KW  - Mapping method
KW  - Weakly similar classes
KW  - Fokker-Planck equations
KW  - Kolmogorov equations
UR  - https://www.sciencedirect.com/science/article/pii/S0022247X22002232
N2  - We revisit the entire framework of group classification of differential equations. After introducing the notion of weakly similar classes of differential equations, we develop the mapping method of group classification for such classes, which generalizes all the versions of this method that have been presented in the literature. The mapping method is applied to group classification of various classes of Kolmogorov equations and of Fokker-Planck equations in the case of space dimension one. The equivalence groupoids and the equivalence groups of these classes are computed. The group classification problems for these classes with respect to the corresponding equivalence groups are reduced to finding all inequivalent solutions of heat equations with inequivalent potentials admitting Lie-symmetry extensions. This reduction allows us to exhaustively solve the group classification problems for the classes of Kolmogorov and Fokker-Planck equations with time-independent coefficients.
ER  - 

OPANASENKO, Stanislav and Roman POPOVYCH. Mapping method of group classification. \textit{Journal of Mathematical Analysis and Applications}. San Diego (USA): Academic Press Inc. Elsevier Science, 2022, vol.~513, No~2, p.~''126209-1''-''126209-43'', 43 pp. ISSN~0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2022.126209.