Abstract

 

Equivalence Transformations of Maxwell Equations in Rigid Bodies

S.Ozer (Department of Engineering Sciences, ITU Faculty of Science and Letters, Istanbul Technical University, Maslak, Istanbul, Turkey); E.Suhuby (Yeditepe University Department of Mathematics, KaydaП, Istanbul, Turkey)

e-mail: ozers@itu.edu.tr

The groups of equivalence transformations for a family of first order equations of the general balance form are investigated. Since the general balance equations involve arbitrary number of independent and dependent variables, their results can be easily applied to all first order partial differential equations. Equivalence groups are much more general than symmetry groups in the sense that they map equations containing arbitrary functions or parameters onto equations of the same structure but with different functions or parameters. Almost all field equations of classical continuum physics possess this property since they describe certain common behaviors of diverse materials.  The method of attack to this problem is based on the exterior calculus. The analysis is reduced to determine isovector fields of an closed ideal of the exterior algebra over an appropriate differentiable manifold dictated by the structure of the differential equations. The determining equations with respect to the isovector field components are obtained and their explicit solutions are determined for the general case. Solutions are applied to the general Maxwell equations of the electrodynamics associated with various constitutive equations.

 

Section : 12