Existence of a solution to the scattering problem for the ultrahyperbolic equation

TL;DR

This paper investigates the existence of solutions to the scattering problem for the ultrahyperbolic equation in Euclidean space, focusing on solutions' behavior at infinity and constructing solutions with prescribed asymptotics.

Contribution

It establishes the existence of solutions to the scattering problem for the ultrahyperbolic equation with specified asymptotic behavior at infinity.

Findings

Solutions with prescribed asymptotics at infinity are constructed.

The behavior of solutions at infinity is characterized.

Existence results are proved for the scattering problem.

Abstract

We consider the ultrahyperbolic equation in the Euclidean space. The behavior at the infinity of a certain class of solutions is studied. We examine the issue of existence of solutions to the scattering problem: for a given asymptotics at the infinity, the corresponding solution to the equation is constructed.