Construction of generalized anisotropic zilch

AbstractConservation equations relating to energy and zilch have recently been generalized to systems of n partial differential equations in n vector-variables. Conditions governing the existence of generalized energy and zilch have been derived. The present investigation extends these concepts to embrace anisotropic conditions, in which 2n vector-variables are related by their curls and time derivatives. Anisotropic symmetric constitutive relations are given, and a search is made for conditions under which reciprocity exists when the reciprocity flux density is expressed in vector product form. The construction of the zilch then rests upon the solution of certain matrix equations, with unknown symmetric and skew-symmetric matrices to be found that contain as many arbitrary constant elements as possible