Quaternionic generalization of telegraph equations

Abstract

Using non-commutative spacetime quaternion algebra, we represent the generalization of one-dimensional and three-dimensional telegraph equations, which are widely applied to consider the propagation of an electromagnetic signal in communication lines, as well as to describe particle diffusion and heat transfer. It is shown that the system of telegraph equations can be represented in compact form as a single quaternion equation taking into account the spacetime properties of physical quantities. The distinctive features of the one-dimensional and three-dimensional telegraph equations are discussed.