At least some differential equations have the equivalent algebraic expressions.
The sets of such (partial) equations are not excluded.
Yes, Dear Prof. Branko V. Mišković
The Maxwell equations for specific cases can be seen as an eight-degree complex polynomial and are not excluded as you state in your thread.
For example in the case of a thin plasma as the one in a stellar corona, check equation 38 in this publication and references therein, please:
Article An Eigenvalue Analysis of Damping in Optical Thin Plasmas
PD. Also in Exploration Geophysics, the AVO amplitude versus offset set of partial differential equations can be seen as a fifth-degree polynomial.
The two relations of J. J. Thomson obey Maxwell's equations.
See: Foundation of Electrodynamics
Prof. Branko V. Mišković yes, if you refer to the discovery by Prof. J.J. Thomson that "the electrons are charge particles" of a "very small mass with negative charge", they obey Maxwell equations.
Best Regards.
The motion of one EM field produces the other of them,
Instead of their variations - in Maxwell's equations.
Therefore, the algebraic relations of J.J. Thomson may be the needed algebraic solution of Maxwell's equations. The differential analysis confirms this.
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