J 2023

Point and generalized symmetries of the heat equation revisited

KOVAL, Serhii D a Roman POPOVYCH

Základní údaje

Originální název

Point and generalized symmetries of the heat equation revisited

Autoři

KOVAL, Serhii D a Roman POPOVYCH (804 Ukrajina, garant, domácí)

Vydání

Journal of Mathematical Analysis and Applications, San Diego (USA), Academic Press Inc. Elsevier Science, 2023, 0022-247X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Journal of Mathematical Analysis and Applications

Kód RIV

RIV/47813059:19610/23:A0000142

Organizační jednotka

Matematický ústav v Opavě

DOI

http://dx.doi.org/10.1016/j.jmaa.2023.127430

UT WoS

001018236500001

Klíčová slova anglicky

Discrete symmetry; Generalized symmetry; Heat equation; Lie symmetry; Point-symmetry pseudogroup; Subalgebra classification

Štítky

Příznaky

Mezinárodní význam, Recenzováno
Změněno: 8. 4. 2024 13:06, Mgr. Aleš Ryšavý

Anotace

V originále

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.
Zobrazeno: 25. 12. 2024 16:10