An Example of a Non-Trivial, Non-Self-Adjoint Huygens Differential Equation in Four Independent Variables

Abstract

A family of non-trivial, essentially non-self-adjoint wave equations which satisfy Huygens' principle is given. It is constructed on a 4-dimensional Lorentzian space which is a product of two 2-dimensional spaces of constant curvature. Prior to this example, the only known non-trivial Huygens equation was the scalar wave equation on the exact plane wave spacetime as presented by Günther.