Another approach to the algebraic classification of electromagnetic field

The usual algebraic classification of the electromagnetic field is known. The classification is connected with an eigenvalues task of the tensor of electromagnetic field. In this case there is a characteristic equation of the fourth order. We can reduce such characteristic equation into a cubic characteristic equation (the normal form of Weierstrass). In the end of our investigation we have a problem of the electromagnetic field classification is an analogous to the Petrov problem of the gravitational field classification. So we have and the analogous algebraic types of the electromagnetic field: I, la, D, N. Prom the point of view of the catastrophes theory the point of phase transition of the second order corresponds to the algebraic type N (a plane electromagnetic wave).