The Cauchy Problem for Non-Archimedean Pseudodifferential Equations of Klein-Gordon Type

TL;DR

This paper introduces a new class of non-Archimedean Klein-Gordon type pseudodifferential equations and analyzes their Cauchy problem, revealing similarities to classical Klein-Gordon equations.

Contribution

It defines and studies a novel class of non-Archimedean Klein-Gordon equations and explores their well-posedness and properties.

Findings

Non-Archimedean Klein-Gordon equations share properties with classical counterparts.

The Cauchy problem for these equations is well-posed.

New insights into non-Archimedean pseudodifferential equations.

Abstract

In this article we introduce a new class of non-Archimedean pseudodifferential equations of Klein-Gordon type and study the corresponding Cauchy problem for these equations. A remarkable fact is that the non-Archimedean Klein-Gordon equations exhibit many similar properties to the classical Klein-Gordon equations.