Fourier analysis of compact oscillons

@misc{klimas2026fourier,
  title = {{Fourier analysis of compact oscillons}},
  author = {Pawel Klimas and Leandro Roza Livramento and João Saldanha Streibel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10746},
  eprint = {2610.10746},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10746},
}

TY  - UNPB
TI  - Fourier analysis of compact oscillons
AU  - Pawel Klimas
AU  - Leandro Roza Livramento
AU  - João Saldanha Streibel
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10746
UR  - https://arxiv.org/abs/2610.10746
AB  - We present a new derivation of the exact compact oscillon in the signum-Gordon model using Fourier methods. This approach decomposes the oscillon into an infinite, uniformly convergent series of discrete modes consisting of a fundamental frequency and its odd higher harmonics, in contrast to standard analytic potentials, where the corresponding infinite perturbative series fails to converge. Crucially, our oscillon evades the non-existence theorem for spatially localized, small-amplitude periodic states. We investigate the accuracy of truncating the Fourier series and find that the primary mode alone provides a remarkably accurate approximation of the exact solution, with agreement improving significantly when the first two non-vanishing harmonic modes are included. Furthermore, we generalize this framework to a swaying compact oscillon with a periodically moving boundary. We show that describing such an oscillon requires even-order modes, whose coupling with the odd source terms induces a dynamic modulation that generates the swaying motion, even though the spatial Fourier profiles themselves are time-independent.
ER  -