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Arbitrariness of the General Solution and Symmetries
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| Reference: Acta Applicandae Mathematicae, 41 (1995) 311-322 |
| Description: Here I applied some of the results obtained in
[5]
to problems related to symmetries. It is well-known that
Lie theory allows us to find only special solutions of a system of
PDEs. I was interested in determining how special these solutions
are, i.e. how much of the solution space we miss. Using the method of
differential constraints this can be done fairly easily for normal
systems. As a second topic I applied the results of
[5]
on gauge symmetries to the Lorentz gauge in
electromagnetism and to harmonic coordinates for the Einstein
equations. |
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