Decay of solutions of wave-type pseudo-differential equations over p-adic fields

TL;DR

This paper investigates the decay behavior of solutions to wave-type pseudo-differential equations over p-adic fields, revealing that their decay resembles that of classical wave equations, thus advancing mathematical understanding of p-adic quantum models.

Contribution

It initiates the study of decay properties of p-adic wave-type pseudo-differential equations, connecting p-adic solutions to classical wave decay behaviors.

Findings

Solutions exhibit decay similar to classical wave equations

Establishes foundational understanding for p-adic wave functions

Bridges p-adic analysis with classical wave phenomena

Abstract

During the eighties several physical models using p-adic numbers were proposed. Particularly various models of p-adic quantum mechanics. As a consequence of this fact several new mathematical problems emerged, among them, the study of p-adic pseudo-differential equations. In this paper we initiate the study of the decay of the solutions of wave-type pseudo-differential equations over p-adic fields; these equations were introduced by Kochubei in connection with the problem of characterizing the p-adic wave functions using pseudo-differential operators. We show that the solutions of p-adic wave-type equations have a decay similar to the solutions of classical generalized wave equations.