Stationary Oscillations in a Damped Wave Equation from Isospectral Bessel Functions

TL;DR

This paper explores the use of isospectral Bessel functions to analyze a damped wave equation, revealing non-typical SUSY behavior and oscillations that persist over time with non-harmonic shapes.

Contribution

It introduces a novel application of isospectral Bessel functions to study damped wave equations, highlighting unique SUSY properties and persistent oscillations.

Findings

Isospectral Bessel functions exhibit non-typical SUSY behavior.

The isospectral partner of the wave equation models a damped system with non-vanishing oscillations.

Oscillations maintain a non-harmonic shape over time.

Abstract

Using the isospectral partners of the Bessel functions derived by Reyes et al., we find, on one hand, that these functions show non-typical supersymmetric (SUSY) behavior and, on the other, that the isospectral partner of the classical wave equation is equivalent to that of a damped system whose oscillations do not vanish in time, but show a non-harmonic shape.