Asymptotic properties of solutions to a certain ultrahyperbolic equation

TL;DR

This paper investigates the long-term behavior of solutions to a generalized ultrahyperbolic equation, analyzing their asymptotic properties at infinity and conditions for their existence with specified asymptotic behavior.

Contribution

It introduces a study of asymptotic properties for solutions to a generalized ultrahyperbolic equation, extending understanding beyond classical equations like Klein-Gordon-Fock.

Findings

Characterization of solution behavior at infinity along timelike directions

Conditions for existence of solutions with prescribed asymptotics

Extension of asymptotic analysis to a generalized ultrahyperbolic framework

Abstract

We consider a certain ultrahyperbolic equation in a Euclidean space being a generalization of Klein-Gordon-Fock equation. The behavior of solutions at points tending to infinity along timelike directions is studied. We examine the issue of existence of solutions possessing given asymptotic properties at infinity.