The Klein–Gordon-equation is a relativistic wave equation, related to the Schrödinger equation. In one space dimension, it is possible to choose units so that

$LaTeX: \frac{\partial^2 u}{\partial t^2} - \frac{\partial^2 u}{\partial x^2} + u = 0$ .

In an MSc thesis from 2024, asymptotics as $LaTeX: \sqrt{t^2-x^2}\to \infty$ for this and related equations were studied, by using a method developed by Lars Hörmander which relies on the method of stationary phase.

In this project, we continue the study of the same equation, but this time by using a Green function which can be written in terms of the Bessel functions LaTeX: J_0 and LaTeX: J_1 . Then we can make use of well known asymptotics for Bessel functions to derive asymptotics for the above equation. The results will hopefully be useful when studying a Klein-Gordon equation with a moving potential.

Kontakt: Sara Maad Sasane