Point and generalized symmetries of the heat equation revisited

@article{78283,
   author = {Koval, Serhii D and Popovych, Roman},
   article_location = {San Diego (USA)},
   article_number = {2},
   doi = {http://dx.doi.org/10.1016/j.jmaa.2023.127430},
   keywords = {Discrete symmetry; Generalized symmetry; Heat equation; Lie symmetry; Point-symmetry pseudogroup; Subalgebra classification},
   language = {eng},
   issn = {0022-247X},
   journal = {Journal of Mathematical Analysis and Applications},
   title = {Point and generalized symmetries of the heat equation revisited},
   url = {https://www.sciencedirect.com/science/article/pii/S0022247X2300433X},
   volume = {527},
   year = {2023}
}

TY  - JOUR
ID  - 78283
AU  - Koval, Serhii D - Popovych, Roman
PY  - 2023
TI  - Point and generalized symmetries of the heat equation revisited
JF  - Journal of Mathematical Analysis and Applications
VL  - 527
IS  - 2
SP  - "127430-1"-"127430-21"
EP  - "127430-1"-"127430-21"
PB  - Academic Press Inc. Elsevier Science
SN  - 0022247X
KW  - Discrete symmetry
KW  - Generalized symmetry
KW  - Heat equation
KW  - Lie symmetry
KW  - Point-symmetry pseudogroup
KW  - Subalgebra classification
UR  - https://www.sciencedirect.com/science/article/pii/S0022247X2300433X
N2  - We derive a nice representation for point symmetry transformations of the (1+1)-dimensional linear heat equation and properly interpret them. This allows us to prove that the pseudogroup of these transformations has exactly two connected components. That is, the heat equation admits a single independent discrete symmetry, which can be chosen to be alternating the sign of the dependent variable. We introduce the notion of pseudo-discrete elements of a Lie group and show that alternating the sign of the space variable, which was for a long time misinterpreted as a discrete symmetry of the heat equation, is in fact a pseudo-discrete element of its essential point symmetry group. The classification of subalgebras of the essential Lie invariance algebra of the heat equation is enhanced and the description of generalized symmetries of this equation is refined as well. We also consider the Burgers equation because of its relation to the heat equation and prove that it admits no discrete point symmetries. The developed approach to point-symmetry groups whose elements have components that are linear fractional in some variables can directly be extended to many other linear and nonlinear differential equations.
ER  - 

KOVAL, Serhii D a Roman POPOVYCH. Point and generalized symmetries of the heat equation revisited. \textit{Journal of Mathematical Analysis and Applications}. San Diego (USA): Academic Press Inc. Elsevier Science, 2023, roč.~527, č.~2, s.~''127430-1''-''127430-21'', 21 s. ISSN~0022-247X. Dostupné z: https://dx.doi.org/10.1016/j.jmaa.2023.127430.