Symmetry Analysis and Exact Similarity Solutions for Maxwellian Equation

Résumé

In this paper, we study the structure of the symmetry algebra associated with the Maxwellian equation which is solvable, non-semi-simple, and non-nilpotent. By adopting Ovsiannikov’s approach which relies on two essential concepts: the adjoint representation and the Killing form. We establish the optimal system in one dimension based on this and the notion of the normalizer of a subalgebra. We then construct the optimal systems in two and three dimensions. By exploiting the structurally significant information derived from these systems, we derive several reduction equations and obtain some exact solutions.