On the arbitrariness of the general solution of an involutive partial differential equation
- 1 January 1994
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 35 (1) , 486-498
- https://doi.org/10.1063/1.530739
Abstract
The relationship between the strength of a differential equation as introduced by Einstein, its Cartan characters, and its Hilbert polynomial is studied. Using the framework of formal theory previous results are extended to nonlinear equations of arbitrary order and to overdetermined systems. The problem of computing the number of arbitrary functions in the general solution is treated. Finally, the effect of gauge symmetries is considered.Keywords
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