Klein-Gordon potential in characteristic coordinates - Т. Ш. Кальменов; Durvudkhan Suragan (Walter de Gruyter GmbH, 2024)
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; Mathematics; Boundary value problem; Domain (mathematical analysis); Mathematical analysis; Cauchy boundary condition; Boundary (topology); Cauchy problem; Potential theory; Kernel (algebra); Mixed boundary condition; Initial value problem; Pure mathematics; Physics; Nonlinear system; Quantum mechanics; type of access: open access