Janet bases and general solutions of Maxwell’s equations in vacuum

By transforming a system of partial differential equations into a Janet basis, one obtains the most comprehensive information regarding its solutions without explicitly determining them. This includes all possible relationships between their derivatives that are not contained in the given system. It also allows for the determination of the so-called differential dimension, which describes the indeterminate elements of a general solution. As a result, the differential equations obtained for the phenomenological description of a physical process may gain a new quality by predicting the discovery of new phenomena. This procedure was applied to Maxwell’s equations in a vacuum. The obtained results can be used to determine explicit expressions for general solutions of Maxwell’s equations that contain the correct number of indeterminate elements. The possible significance for the physical quantities involved was briefly discussed. A similar procedure can be applied to any system of partial differential equations.