Electrodymanics with Toroid Polarization
  A modified system of equations of electrodynamics has been obtained. Beside the Lagrangian one an alternative gauge-like formalism has been developed to introduce the toroid moment contributions in the equations obtained. The two potential formalism that was worked out by us earlier has been developed further where along with the two vector potentials we introduce two scalar potentials thus taking into account all the four equations of electromagnetism. 
V.M. Dubovik and B. Saha