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Extended group analysis of the wave equation

University of British Columbia

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.

Text

2010-10-21

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http://hdl.handle.net/2429/29420

Mathematics

University of British Columbia

Graduate