Point and generalized symmetries of the heat equation revisited

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F23%3AA0000142" target="_blank" >RIV/47813059:19610/23:A0000142 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022247X2300433X?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X2300433X?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2023.127430" target="_blank" >10.1016/j.jmaa.2023.127430</a>

Result language
angličtina
Original language name
Point and generalized symmetries of the heat equation revisited
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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