KOVAL, Serhii D and Roman POPOVYCH. Point and generalized symmetries of the heat equation revisited. Journal of Mathematical Analysis and Applications. San Diego (USA): Academic Press Inc. Elsevier Science, 2023, vol. 527, No 2, p. "127430-1"-"127430-21", 21 pp. ISSN 0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2023.127430.
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Basic information
Original name Point and generalized symmetries of the heat equation revisited
Authors KOVAL, Serhii D and Roman POPOVYCH (804 Ukraine, guarantor, belonging to the institution).
Edition Journal of Mathematical Analysis and Applications, San Diego (USA), Academic Press Inc. Elsevier Science, 2023, 0022-247X.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW Journal of Mathematical Analysis and Applications
RIV identification code RIV/47813059:19610/23:A0000142
Organization unit Mathematical Institute in Opava
Doi http://dx.doi.org/10.1016/j.jmaa.2023.127430
UT WoS 001018236500001
Keywords in English Discrete symmetry; Generalized symmetry; Heat equation; Lie symmetry; Point-symmetry pseudogroup; Subalgebra classification
Tags MÚ
Tags International impact, Reviewed
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 8/4/2024 13:06.
Abstract
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.
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