ENERGY-MOMENTUM-DIRECTED NONLINEARIZATION OF MAXWELLS EQUATIONS IN THE CASE OF A CONTINUOUS MEDIA

This paper extends the ideas of Donev & Tashkova (1993) to a relativis tic nonlinearization of the classical Maxwell theory in the continuous medium case. The field here is described by a 2-form on Minkowski spa ce with values in a two-dimensional vector space V having F and F as components. The vacuum equations are written in these terms. The react ion of the medium in the sense of energy-momentum exchange with the fi eld is assumed to be described by two V-valued 1-forms Phi and Psi, an d equations, considering how this exchange is performed, are written d own. Any couple of the four components of Phi and Psi is assumed to de fine a completely integrable Pfaff system. Maxwell theory for continuo us media is obtained as a special case. A large set of non-Maxwellian solutions, generated by any solution of the general (1 + 1) evolution equation V-t = L[V] and two functions g(x) and h(y), is found. The (3 + 1)-soliton-like solutions are briefly discussed.