Equivalence groups for first-order balance equations and applications to electromagnetism. (English) Zbl 1178.78003
Theor. Math. Phys. 137, No. 2, 1590-1597 (2003); translation from Teor. Mat. Fiz. 137, No. 2, 271-280 (2003).
Summary: We investigate the groups of equivalence transformations for first-order balance equations involving an arbitrary number of dependent and independent variables. We obtain the determining equations and find their explicit solutions. The approach to this problem is based on a geometric method that depends on Cartan’s exterior differential forms. The general solutions of the determining equations for equivalence transformations for first-order systems are applied to a class of the Maxwell equations of electrodynamics.
MSC:
78A25 | Electromagnetic theory (general) |
35A30 | Geometric theory, characteristics, transformations in context of PDEs |
35Q60 | PDEs in connection with optics and electromagnetic theory |