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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@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 and 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, 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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