Differential homomorphisms of linear homogeneous systems of differential equations

Abstract

Linear differential operators with complex-valued infinitely differentiable coefficients, linear homogeneous systems of differential equations, and modules over algebras of scalar linear differential operators are considered. Linear differential changes of variables and homomorphisms of special quotient modules (differential homomorphisms) generated by these changes are studied. In terms of differential homomorphisms, relationships between Maxwell equations and equations of electromagnetic potential and between Dirac equations and the Klein-Gordon system of independent equations are described. It is proved that all ordinary nondegenerate linear homogeneous differential equations of some common order and the homogeneous normal systems of the same common order are differentially isomorphic.