Klein-Gordon potential in characteristic coordinates

Abstract

By the Klein-Gordon potential, we call a convolution-type integral with a kernel, which is the fundamental solution of the Klein-Gordon equation and also a solution of the Cauchy problem to the same equation. An interesting question having several important applications (in general) is what boundary condition can be imposed on the Klein-Gordon potential on the boundary of a given domain so that the Klein-Gordon equation with initial conditions complemented by this “transparent” boundary condition would have a unique solution within that domain still given by the Klein-Gordon potential. It amounts to finding the trace of the Klein-Gordon potential to the boundary of the given domain. In this article, we analyze this question and construct a novel initial boundary-value problem for the Klein-Gordon equation in characteristic coordinates.

Keywords

• klein-gordon equation
• wave equation
• cauchy problem
• characteristic coordinates
• 35l05
• 35a08
• 47g40
• 81q05