On the spectrum of a waveguide with periodic cracks

TL;DR

This paper investigates the spectral properties of a waveguide with periodic cracks, deriving asymptotic dispersion relations assuming small crack openings, which advances understanding of wave behavior in such structured media.

Contribution

It provides the first asymptotic analysis of dispersion relations for waveguides with periodic cracks under small opening assumptions.

Findings

Derived asymptotic dispersion relations for small crack openings.

Identified how periodic cracks influence wave propagation.

Provided mathematical framework for spectral analysis of cracked waveguides.

Abstract

The spectral problem on a periodic domain with cracks is studied. An asymptotic form of dispersion relations is calculated under assumption that the opening of the cracks is small.