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Extended group analysis of the wave equation

A comprehensive study of potential symmetries admitted by partial differential equations
is given using the wave equation utt = c²(x)uxx as a given prototype equation, R. Methods are given for the construction of various conserved forms for R. Potential symmetries
for R are nonlocal symmetries realized as local symmetries of auxiliary systems obtained from conserved forms of R. The existence of potential symmetries for R can be determined algorithmically and automatically by the use of a symbolic manipulation program. Most importantly, the potential symmetries obtained through one auxiliary system may or may not include and/or extend those obtained through another auxiliary system. The work in this thesis significantly extends the previously known classes of potential symmetries admitted by R and results in a better understanding of the limits in the construction of potential symmetries for R. / Science, Faculty of / Mathematics, Department of / Graduate

Identiferoai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/29420
Date January 1990
CreatorsMa, Alex Yim-Cheong
PublisherUniversity of British Columbia
Source SetsUniversity of British Columbia
LanguageEnglish
Detected LanguageEnglish
TypeText, Thesis/Dissertation
RightsFor non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

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