On a certain representation of a solution to the characteristic problem for the ultrahyperbolic equation

TL;DR

This paper studies the characteristic problem for the ultrahyperbolic equation, establishing a well-posed framework and deriving a solution representation useful for asymptotic analysis at infinity.

Contribution

It introduces a well-posed formulation for the characteristic problem and provides a new representation of solutions for asymptotic analysis.

Findings

Established a well-posed set-up for the characteristic problem.

Derived a solution representation suitable for asymptotic analysis.

Facilitated understanding of solution behavior at infinity.

Abstract

We consider the characteristic problem for the ultrahyperbolic equation in the Euclidean space. The value of a solution is prescribed on the characteristic hyperplane. A well-posed set-up of the problem is discussed. We obtain a certain representation for a solution suitable for analysis of its asymptotics at the infinity.