Wave pulses with unusual asymptotical behavior at infinity

TL;DR

This paper investigates wave signals with atypical slow decay at large distances, providing physical explanations, examples, and proofs of feasible electromagnetic and acoustic fields exhibiting such unusual asymptotic behavior.

Contribution

It introduces new scalar wave solutions with slower decay than inverse distance, expanding understanding of wave behavior at infinity.

Findings

Examples of scalar wave pulses with abnormal slow decay

Physical explanations for unusual asymptotic behavior

Feasibility proofs for acoustic and electromagnetic fields with slow decay

Abstract

The behavior of wave signals in the far zone is not only of theoretical interest but also of paramount practical importance in communications and other fields of applications of optical, electromagnetic or acoustic waves. Long time ago T. T. Wu introduced models of 'electromagnetic missiles' whose decay could be made arbitrarily slower than the usual inverse distance by an appropriate choice of the high frequency portion of the source spectrum. Very recent work by Plachenov and Kiselev introduced a finite-energy scalar wave solution, different from Wu's, decaying slower than inversely proportional with the distance. A physical explanation for the unusual asymptotic behavior of the latter will be given in this article. Furthermore, two additional examples of scalar wave pulses characterized by abnormal slow decay in the far zone will be given and their asymptotic behavior will be discussed. A proof of feasibility of acoustic and electromagnetic fields with the abnormal asymptotics will be described.