Local reduction of certain wave operators to one-dimensional form Original Research Article

In this paper, we point out an interesting fact concerning three common instances of linear wave propagation (acoustic, electromagnetic, and elastic). In each case, we consider the initial-value problem in some region of space sufficiently small that the gradients in the data can be taken as constant. Then the evolution of that data in time corresponds precisely to that produced by one-dimensional waves travelling in some distinguished direction. In the three instances, this direction is defined by the pressure gradient, by View the MathML source (not the Poynting vector), and by any vector perpendicular to View the MathML source. We also consider an abstract system, to which all 2 × 2 systems in a certain class are equivalent.